Limited Consent to Credit Agreement and Guaranty

Exhibit 10.4

Execution Version

LIMITED CONSENT TO CREDIT AGREEMENT AND GUARANTY

THIS LIMITED CONSENT TO CREDIT AGREEMENT AND GUARANTY (this “Agreement”) is made as of September 28, 2026, by and among TELA BIO, INC., a Delaware corporation (the “Borrower”), the Lenders party hereto (constituting Required Lenders under the Credit Agreement (as defined below), the “Consenting Lenders”) and PERCEPTIVE CREDIT HOLDINGS V, LP, a Delaware limited partnership, as administrative agent and collateral agent for the Lenders (in such capacities, together with its successors and assigns in such capacities, the “Administrative Agent”). Capitalized terms used in this Agreement (including this Preamble and the Recitals), to the extent not otherwise defined herein, shall have the same meaning as in the Credit Agreement.

RECITALS

WHEREAS, the Borrower is party to that certain Credit Agreement and Guaranty, dated as of November 13, 2025 (as amended, restated, amended and restated, supplemented or otherwise modified from time to time prior to the date hereof, the “Credit Agreement”), by and among the Borrower, the Administrative Agent and the Lenders party thereto from time to time, pursuant to which, among other things, the Lenders have made certain loans and financial accommodations available to the Borrower;

WHEREAS, pursuant to Section 10.02 of the Credit Agreement, the Borrower is required to maintain minimum Revenue of $80,800,000 and $86,300,000 for the trailing twelve consecutive month periods ending on September 30, 2026, and December 31, 2026, respectively (collectively, the “Q3 & Q4 ‘26 Minimum Revenue”);

WHEREAS, the Borrower has requested that, subject to the terms and conditions set forth herein, the Administrative Agent and the Consenting Lenders agree that the Q3 & Q4 ‘26 Minimum Revenue shall not be tested pursuant to Section 10.02 of the Credit Agreement;

WHEREAS, pursuant to Section 14.04 of the Credit Agreement, the consent set forth herein requires the written consent of the Borrower, the Administrative Agent and the Consenting Lenders; and

WHEREAS, Administrative Agent and the Consenting Lenders are willing to grant the requested consent subject to the terms and conditions set forth herein.

NOW, THEREFORE, in consideration of the premises set forth above, the terms and conditions contained herein and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto agree as follows:

1.Limited Consent.   Subject to the terms and conditions and relying upon the representations and warranties set forth herein, the Administrative Agent and the Consenting Lenders hereby agree that, notwithstanding Section 10.02 of the Credit Agreement to the contrary, the minimum Revenue financial covenant set forth therein shall not be tested for the periods ending on or about September 30, 2026 or December 31, 2026. This Agreement is specific as to content and time and shall not constitute a consent to departure from or a waiver of any other current or future default or breach of any other terms in the Credit Agreement or any other Loan Documents. The foregoing consent shall also not be deemed to operate as or obligate the Administrative Agent or the Lenders to grant any future waiver, modification of or consent to any other term, condition or Default under the Credit Agreement. Nothing contained herein shall constitute a course of conduct or dealing among the parties.

2.Conditions Precedent to Effectiveness of this Agreement.   This Agreement shall become effective upon the satisfaction of all of the following conditions precedent or waiver thereof by the Lenders

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(such date, the “Consent Effective Date”):

(a)The Administrative Agent shall have received counterparts of this Agreement, executed by the Borrower, the Administrative Agent and the Lenders.

(b)The representations and warranties set forth in Section 3 hereof shall be true and correct as of the date hereof.

(c)[reserved].

(d)The Borrower shall have paid all amounts owing pursuant to the terms of Section 14.03 of the Credit Agreement for which the Administrative Agent has provided an invoice to the Borrower at least one (1) Business Day prior to the Consent Effective Date.

3.Representations and Warranties.   The Borrower represents and warrants to the Administrative Agent and the Lenders as follows:

(a)Organization; Powers; Governmental Approvals; No Conflicts. The execution and delivery by the Borrower of this Agreement and the performance by the Borrower of the Loan Documents (as modified hereby) to which it is a party (i) are within its corporate or other organizational powers, (ii) have been duly authorized by all necessary corporate or other organizational action, (iii) do not require any consent or approval of, registration or filing with, or any other action by, any Governmental Authority, except for those that have been obtained or made and are in full force and effect, and filings created pursuant to the Security Documents, (iv) will not violate the Borrower’s Organizational Documents or any Law applicable to the Borrower, and (v) will not violate or result in a default under any Material Agreement, or give rise to a right thereunder to require any payment to be made by any such Person.

(b)Binding Effect. This Agreement and each other Loan Document (as modified hereby) to which Borrower is a party has been duly executed and delivered by the Borrower and is a legal, valid and binding obligation of the Borrower, enforceable in accordance with its terms, except as such enforceability may be limited by (i) bankruptcy, insolvency, reorganization, moratorium or similar Laws of general applicability affecting the enforcement of creditors’ rights, and (ii) the application of general principles of equity (regardless of whether such enforceability is considered in a proceeding in equity or at law).

(c)Representations and Warranties. The representations and warranties of the Borrower contained in each Loan Document are true, correct and complete in all material respects (without duplication of any materiality qualifier contained therein) on and as of the date hereof (with the same effect as though made on and as of the date hereof); provided that (x) all representations and warranties set forth in each Loan Document that are qualified by materiality or Material Adverse Effect or the like are, in each case, true and correct in all respects as of the date hereof; provided that to the extent that such representations and warranties specifically refer to an earlier date, they shall be true and correct in all respects as of such earlier date, and (y) the representations and warranties set forth in each Loan Document that are not qualified by materiality, Material Adverse Effect or the like are, in each case, true and correct in all material respects as of the date hereof; provided that to the extent that such representations and warranties specifically refer to an earlier date, they shall be true and correct in all material respects as of such earlier date.

(d)No Default. No Default or Event of Default has occurred and is continuing immediately before or immediately after giving effect to this Agreement and the transactions contemplated hereby.

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4.Governing Law; Jurisdiction.   THIS AGREEMENT AND ANY CLAIM, CONTROVERSY OR DISPUTE ARISING UNDER OR RELATED TO THIS AGREEMENT, WHETHER IN TORT, CONTRACT (AT LAW OR IN EQUITY) OR OTHERWISE, SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAW OF THE STATE OF NEW YORK, WITHOUT REGARD TO PRINCIPLES OF CONFLICTS OF LAWS THAT WOULD RESULT IN THE APPLICATION OF THE LAWS OF ANY OTHER JURISDICTION; PROVIDED THAT SECTION 5-1401 OF THE NEW YORK GENERAL OBLIGATIONS LAW SHALL APPLY. EACH PARTY HERETO HEREBY AGREE THAT ANY SUIT, ACTION OR PROCEEDING WITH RESPECT TO THIS AGREEMENT OR ANY OTHER LOAN DOCUMENT TO WHICH IT IS A PARTY OR ANY JUDGMENT ENTERED BY ANY COURT IN RESPECT THEREOF MAY BE BROUGHT INITIALLY IN THE FEDERAL OR STATE COURTS IN NEW YORK, NEW YORK OR IN THE COURTS OF ITS OWN CORPORATE DOMICILE AND IRREVOCABLY SUBMITS TO THE NON-EXCLUSIVE JURISDICTION OF EACH SUCH COURT FOR THE PURPOSE OF ANY SUCH SUIT, ACTION, PROCEEDING OR JUDGMENT.

5.WAIVER OF JURY TRIAL.   EACH PARTY HERETO HEREBY IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY AND ALL RIGHT TO TRIAL BY JURY IN ANY SUIT, ACTION OR PROCEEDING ARISING OUT OF OR RELATING TO THIS AGREEMENT, THE OTHER LOAN DOCUMENTS OR THE TRANSACTIONS CONTEMPLATED HEREBY OR THEREBY.

6.Venue; Consent to Service of Process.   Each of the parties hereto hereby agrees that each of Sections 14.10(a), 14.10(b) and 14.10(c) of the Credit Agreement is incorporated by reference herein, mutatis mutandis, and shall have the same force and effect with respect to this Agreement as if originally set forth herein.

7.Amendments; Counterparts; Integration.   This Agreement may be executed in any number of counterparts, all of which taken together shall constitute one and the same instrument and any of the parties hereto may execute this Agreement by signing any such counterpart. Delivery of an executed signature page of this Agreement by electronic transmission (in PDF format) shall be effective as delivery of a manually executed counterpart hereof. Any signature (including, without limitation, (x) any electronic symbol or process attached to, or associated with, a Contract or other record and adopted by a Person with the intent to sign, authenticate or accept such Contract or record and (y) any pdf signature) hereto, and any contract formation or record-keeping, in each case, through electronic means, shall have the same legal validity and enforceability as a manually executed signature or use of a paper-based record-keeping system to the fullest extent permitted by applicable Law, including the Federal Electronic Signatures in Global and National Commerce Act, the New York State Electronic Signatures and Records Act, or any similar state Law based on the Uniform Electronic Transactions Act, and the parties hereto hereby waive any objection to the contrary.

8.Reference to and Effect on the Loan Documents.

(a)Upon and after the effectiveness of this Agreement, each reference in the Credit Agreement to “this Agreement”, “hereunder”, “hereof” or words of like import referring to the Credit Agreement, and each reference in the other Loan Documents to “the Credit Agreement”, “thereof” or words of like import referring to the Credit Agreement, shall mean and be a reference to the Credit Agreement as modified by this Agreement.

(b)Except as specifically set forth in this Agreement, the Credit Agreement and all other Loan Documents, are and shall continue to be in full force and effect and are hereby in all respects ratified and confirmed and shall constitute the legal, valid, binding and enforceable obligations of the

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Borrower to the Administrative Agent and the Lenders without defense, offset, claim or contribution.

(c)The execution, delivery and effectiveness of this Agreement shall not, except as expressly provided herein, operate as a waiver of any right, power or remedy of the Administrative Agent or any Lender under any of the Loan Documents, nor constitute a waiver of any provision of any of the Loan Documents.

9.Ratification.   The Borrower hereby ratifies and reaffirms each and every term and condition set forth in the Credit Agreement, as modified by this Agreement, and the other Loan Documents effective as of the date hereof, including, without limitation, the grant of security interests and liens by the Borrower under the Collateral Documents and confirms and agrees that such security interests and liens are and shall remain in full force and effect to secure all of the Obligations, including as modified hereby, in accordance with the terms of the Loan Documents. The validity and enforceability of any appointment of the Administrative Agent as proxy or attorney-in-fact under any Loan Document is ratified and reaffirmed as of the date hereof, and the Borrower reappoints the Administrative Agent as its proxy and attorney-in-fact in accordance with the terms of the Loan Documents, as applicable, which appointment is IRREVOCABLE and coupled with an interest until the Termination Date, for the purpose of carrying out the provisions of the Loan Documents, as applicable. Each Guarantor hereby ratifies and reaffirms its guaranty of the Obligations pursuant to the Loan Documents. In furtherance of the above, the Borrower hereby authorizes Administrative Agent to file one or more financing or continuation statements, and amendments thereto (or similar documents required by any laws of any applicable jurisdiction), relating to all or any part of the Collateral without the signature of the Borrower (to the extent such signature is required under the laws of any applicable jurisdiction), which financing statements may describe the Collateral as “all assets”, “all assets of the Debtor, whether now owned or existing or hereafter acquired or arising and regardless of where located” or “all personal property” or words of like import.

10.Severability.   To the extent permitted by law, any provision of this Agreement held to be invalid, illegal or unenforceable in any jurisdiction shall, as to such jurisdiction, be ineffective to the extent of such invalidity, illegality or unenforceability without affecting the validity, legality and enforceability of the remaining provisions thereof; and the invalidity of a particular provision in a particular jurisdiction shall not invalidate such provision in any other jurisdiction.

11.Status as a Loan Document.   This Agreement constitutes a Loan Document.

12.Captions. The section headings of this Agreement are for purposes of reference only and shall not limit or otherwise affect the meaning hereof.

13.No Novation.   By its execution of this Agreement, each of the parties hereto acknowledges and agrees that the terms of this Agreement do not constitute a novation, but, rather, a supplement of the terms of a pre-existing indebtedness and related agreement, as evidenced by the Credit Agreement.

14.Release of Claims.   The Borrower hereby acknowledges and agrees that as of the date hereof: (a) neither it nor any of its Subsidiaries has any claim or cause of action against the Administrative Agent or any Lender (or any of the directors, officers, employees, agents, attorneys or consultants of any of the foregoing), and (b) the Administrative Agent and the Lenders have heretofore properly performed and satisfied in a timely manner all of their obligations to the Borrower, and all of their Subsidiaries and Affiliates. Notwithstanding the foregoing, the Administrative Agent and the Lenders wish (and the Borrower agrees) to eliminate any possibility that any past conditions, acts, omissions, events or circumstances would impair or otherwise adversely affect any of their rights, interests, security and/or remedies. Accordingly, for and in consideration of the agreements contained in this Agreement and other good and valuable consideration, the Borrower (for itself and its Subsidiaries and Affiliates and the

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successors, assigns, heirs and representatives of each of the foregoing) (collectively, the “Releasors”) does hereby fully, finally, unconditionally and irrevocably release, waive and forever discharge the Administrative Agent and the Lenders, together with their respective Affiliates and Related Funds, and each of the directors, officers, employees, agents, attorneys and consultants of each of the foregoing (collectively, the “Released Parties”), from any and all debts, claims, allegations, obligations, damages, costs, attorneys’ fees, suits, demands, liabilities, actions, proceedings and causes of action, in each case, whether known or unknown, contingent or fixed, direct or indirect, and of whatever nature or description, and whether in law or in equity, under contract, tort, statute or otherwise, which any Releasor has heretofore had or now or hereafter can, shall or may have against any Released Party by reason of any act, omission or thing whatsoever done or omitted to be done, in each case, on or prior to the Consent Effective Date directly arising out of, connected with or related to this Agreement, the Credit Agreement or any other Loan Document, or any act, event or transaction related or attendant thereto, or the agreements of the Administrative Agent or any Lender contained therein, or the possession, use, operation or control of any of the assets of the Borrower, or the making of any Loans or other advances, or the management of such Loans or other advances or the Collateral (each individually, a “Claim”). The Borrower represents and warrants that it has no knowledge of any Claim by any Releasor against any Released Party or of any facts or acts or omissions of any Released Party which on the date hereof would be the basis of a Claim by any Releasor against any Released Party which would not be released hereby. Further, each Releasor hereby (i) expressly agrees that the release contemplated by the foregoing Section 14 extends to any and all rights granted under Section 1542 of the California Civil Code (“Section 1542”) or any analogous state law or federal law or regulation, and (ii) expressly waives the benefit of Section 1542 and any analogous state law or federal law or regulation. Section 1542 reads as follows:

“A GENERAL RELEASE DOES NOT EXTEND TO CLAIMS WHICH THE CREDITOR OR RELEASING PARTY DOES NOT KNOW OR SUSPECT TO EXIST IN HIS OR HER FAVOR AT THE TIME OF EXECUTING THE RELEASE AND THAT, IF KNOWN BY HIM OR HER, WOULD HAVE MATERIALLY AFFECTED HIS OR HER SETTLEMENT WITH THE DEBTOR OR RELEASED PARTY.”

Without limiting the generality of the foregoing, each Releasor hereby covenants and agrees from and after the date hereof (i) not to file, or permit any other Releasor to file, any claim, complaint or cause of action, and (ii) not to commence, or permit any other Releasor to commence, any suit, action, arbitration or other proceedings with any court, arbitration forum, regulatory or administrative agency, with respect to any Claim released pursuant to this Section 14.

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be duly executed by their respective authorized officers as of the day and year first above written.

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[Signature Page to Limited Consent to Credit Agreement and Guaranty]

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[Signature Page to Limited Consent to Credit Agreement and Guaranty]