That's altering a contract. If there's a dispute about added terms (that both parties signed) it's usually construed against the more sophisticated party, i.e. the bank, not the customer.

What this dude is trying to do is from the UCC chapter 3 on negotiable instruments, which are checks and drafts. What most people know as checks are called drafts.

Accord and satisfaction: it's funny, because is one of the rare times in law when the magic words have to be exact, and the phrase is "tendered in full satisfaction" or in full satisfaction. If the check says that in the memo line (if check is to you) or under an endorsement (if it was signed over to you), and you cash it after, you have liquidated the debt subject to certain limitations; i.e., if the organization tenders repayment back to you, the underlying promissory obligation is unpaused.

https://www.law.cornell.edu/ucc/3/3-311

Usually a draft have to be a naked order, directed to your bank, to pay the bearer or assignee, and nothing more. But this is one of the few exceptions to what you can write on a check and have the check still be valid.

§ 3-311. ACCORD AND SATISFACTION BY USE OF INSTRUMENT.

(a) If a person against whom a claim [for payment of the underlying contractual obligation] is asserted proves that; (i) that person in good faith tendered an instrument to** the claimant as full satisfaction of the claim,** (ii) the amount of the claim was unliquidated or subject to a bona fide dispute, and (iii) the claimant obtained payment of the instrument, the following subsections apply.

(b) Unless subsection (c) applies, the claim is discharged if the person against whom the claim is asserted proves that the instrument or an accompanying written communication contained a conspicuous statement to the effect that the instrument was tendered as full satisfaction of the claim.

(c) Subject to subsection (d), a claim is not discharged under subsection (b) if either of the following applies:

(1) The claimant, if an organization, proves that (i) within a reasonable time before the tender, the claimant sent a conspicuous statement to the person against whom the claim is asserted that communications concerning disputed debts, including an instrument tendered as full satisfaction of a debt, are to be sent to a designated person, office, or place, and (ii) the instrument or accompanying communication was not received by that designated person, office, or place.

(2) The claimant, whether or not an organization, proves that within 90 days after payment of the instrument, the claimant tendered repayment of the amount of the instrument to the person against whom the claim is asserted. This paragraph does not apply if the claimant is an organization that that sent a statement complying with paragraph (1)(i).

(d) A claim is discharged if the person against whom the claim is asserted proves that within a reasonable time before collection of the instrument was initiated, the claimant, or an agent of the claimant having direct responsibility with respect to the disputed obligation, knew that the instrument was tendered in full satisfaction of the claim.