You are responsible for the 2 extra days, however, it looks like the law is on your side and you may not have to pay it. I may be way off though, I don't have any law experience and this stuff is hard to read.
You need to read
1303.40. (UCC 3-311) Accord and satisfaction by use of instrument.
I did find this explanation that may help
http://www.omeda.org/fastfacts/1150.htm
OHIO -- ACCEPTANCE OF PAYMENT-IN-FULL CHECKS
Any business, especially those that accept a large number of checks, should be aware of ORC 1303.40, effective August 19, 1994. ORC 1303.40, based on UCC 3-311, defines the rules governing checks intended for the accord and satisfaction of debts that are disputed or unliquidated, also known as "payment in full" checks. Debtors make the checks out for less than the full amount due and either mark the check with a phrase such as "payment in full" or include a written statement explaining that the check represents an amount intended to be full satisfaction of the debt. Today, any business that accepts such checks may be accepting cancellation of the remaining debt.
Like Ohio's common law rule of accord and satisfaction, the general rule of ORC 1303.40 is that a creditor's acceptance of a "payment in full" check, tendered in good faith by the debtor is full satisfaction of the debt and any additional claim against the debtor is precluded. "Good faith" is defined in ORC section 1301.01(S) as "honest in fact in the conduct or transaction concerned." The debtor, therefore, still has the burden of demonstrating that the dispute over the amount in question is based on some legitimate issue and not merely a desire to receive something for nothing.
The general rule that acceptance of the check discharges any further claims against the debtor is subject to two statutory exceptions. First, a claim is not discharged if the creditor, within a reasonable time before the debtor receives the payment in full check, sent a conspicuous statement to the person that any communication concerning disputed debts must be sent to a designated person, office, or place and the check was not received by the person, office, or place so designated.
Second, if the first exception does not apply, a claim is not discharged if the creditor tenders repayment of the amount of the instrument to the debtor within ninety days after payment of the check.
Despite the exceptions, however, a claim may still be discharged by the payment in full check if the creditor or an agent of the creditor that is directly responsible for the disputed payment knew that the instrument was tendered in full satisfaction of the debt within a reasonable time before collection of the instrument was initiated. An agent of the creditor includes employees, collection agencies, attorneys, finance companies, and any other person or agency that is responsible for collecting delinquent debts. Acceptance of the check by any of the foregoing will discharge the remainder of the debt regardless of the two exceptions. On the other hand, payments sent to lockboxes will not preclude a claim for the remaining debt because the clerks processing the checks do not have "direct responsibility with respect to the disputed obligation."
To avoid the discharge of claims against debtors, businesses accepting a large number of checks should examine their current check receipt and deposit procedures and implement new procedures aimed at solving problems presented by the new law. Specifically, businesses should: 1) include language on its billing statements or documents directing payments for disputed claims to a specific person, office or place and 2) make sure that the creditor or its agents are capable of discovering and tendering repayment within ninety (90) days after a payment in full check has been received or deposited. Additionally, businesses should make sure that their employees and any other person or entity assigned to collect their debts are aware that payment in full checks should not be accepted or deposited because acceptance will result in a discharge of the debt.