Exhibit 10.3

June 30, 2026

Leonite Fund I, LP
600 East Crescent Avenue, Suite 104
Upper Saddle River, New Jersey 07458
Attention: Avi Geller

Ladies and Gentlemen:

OS Therapies Incorporated, a Delaware corporation (the “Company”), certain wholly owned subsidiaries of the Company and Leonite Fund I, LP, a Delaware limited partnership (the “Investor”), are parties to that certain Securities Purchase Agreement, dated as of June 30, 2026 (the “Purchase Agreement”), pursuant to which the Company agreed to, among other things, issue to the Investor (i) a senior secured convertible promissory note in the principal amount of up to $10,000,000 (the “Note”), to be funded in one or more tranches, and (ii) a warrant to purchase up to 1,750,000 shares of the Company’s common stock (the “Warrant” and, collectively with the Note, the Purchase Agreement and the other agreements, instruments and documents delivered in connection therewith, the “Transaction Documents”). Capitalized terms used but not otherwise defined herein shall have the meanings ascribed to such terms in the Note, the Warrant or the Purchase Agreement, as applicable.

Section 2.2(b)(4) of the Note provides that, among other things, such Section applies only to a Dilutive Issuance (as defined in the Note) occurring after July 1, 2026, and no sale, grant, disposition, amendment, announcement, filing or other event occurring prior to July 1, 2026 shall constitute or be deemed to constitute a Dilutive Issuance or otherwise give rise to any adjustment under Section 2.2(b)(4) of the Note. Notwithstanding anything to the contrary in the Note, the parties hereby agree that any Dilutive Issuance shall constitute a Dilutive Issuance for all purposes under Section 2.2(b)(4) of the Note; provided, however, that no adjustment under Section 2.2(b)(4) of the Note arising from any Dilutive Issuance shall become effective on or prior to September 29, 2026. Any adjustment under Section 2.2(b)(4) of the Note arising from a Dilutive Issuance occurring on or prior to September 29, 2026 shall be determined in accordance with the terms of the Note as of the date of such Dilutive Issuance, but shall automatically become effective on September 30, 2026, without any further action by any party.

Section 2(c) of the Warrant provides that, among other things, such Section applies only to a Dilutive Issuance (as defined in the Warrant) occurring after July 1, 2026, and no sale, grant, disposition, amendment, announcement, filing or other event occurring on or prior to July 1, 2026 shall constitute a Dilutive Issuance or give rise to any adjustment under Section 2(c) of the Warrant. Notwithstanding anything to the contrary in the Warrant, the parties hereby agree that any Dilutive Issuance shall constitute a Dilutive Issuance for all purposes under Section 2(c) of the Warrant; provided, however, that no adjustment under Section 2(c) of the Warrant arising from any Dilutive Issuance shall become effective on or prior to September 29, 2026. Any adjustment under Section 2(c) of the Warrant arising from a Dilutive Issuance occurring on or prior to September 29, 2026 shall be determined in accordance with the terms of the Warrant as of the date of such Dilutive Issuance, but shall automatically become effective on September 30, 2026, without any further action by any party.

The parties acknowledge that certain provisions of the Transaction Documents, including, without limitation, Sections 4.13 (Right of First Refusal), 4.14 (Terms of Future Financings) and 4.16 (Rollover Rights) of the Purchase Agreement and the Warrant, contain certain carve-outs or exceptions. Notwithstanding anything to the contrary in the Purchase Agreement, the Note, the Warrant or any other Transaction Document, the parties hereby agree that each carve-out or exception set forth in any Transaction Document relating to an offering resulting in, or reasonably expected to result in, gross proceeds to the Company of at least $5,000,000 shall apply only to an offering in which gross proceeds to the Company of at least $5,000,000 are received in a single closing, and gross proceeds received across multiple closings, tranches or separate offerings shall not be aggregated for purposes of satisfying such $5,000,000 threshold.

Except as expressly modified by this letter agreement, the Note, the Warrant and the other Transaction Documents shall remain unchanged, unmodified and in full force and effect in accordance with their respective terms. Nothing contained herein shall be deemed to constitute a waiver of any right of the Investor or an obligation of the Company under the Transaction Documents.

In the event of any conflict or inconsistency between the provisions of this letter agreement and the provisions of the Note or the Warrant with respect to the subject matter hereof, the provisions of this letter agreement shall control and govern.

This letter agreement shall be governed by and construed in accordance with the laws of the State of Delaware, without regard to its conflict of laws principles. The governing law, dispute resolution, arbitration, equitable relief, receiver, security-interest enforcement, forum selection, jurisdiction, service of process, waiver of jury trial, venue and related remedies provisions set forth in the Purchase Agreement are hereby incorporated by reference into this letter agreement, mutatis mutandis, and shall apply to this letter agreement as if set forth herein in full.

This letter agreement may be executed in one or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same agreement. Signatures delivered by electronic mail (including .pdf or any electronic signature complying with the U.S. federal ESIGN Act of 2000) or other electronic transmission shall be deemed original signatures for all purposes.

If the foregoing accurately reflects the agreement between the parties, please indicate your acceptance by executing this letter agreement in the space provided below. This letter agreement shall be effective as of date hereof upon execution and delivery by each of the parties hereto.

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AGREED AND ACCEPTED
as of the date first written above:

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