I do not know how big the company is, but if it is large company it would cause a lot of confusion if you send them money that they are not pursuing. In fact, the money might not even be applied properly even if they cash your check. You might end up having to go through all kinds of legal hoops anyway to prove that you repaid them.
I would recommend putting the money aside in a savings account until they actually ask you for it if they are a large company. If they are a small or smaller company I would not give them the money until or unless they are willing to exchange a written release of the debt in exchange for the check.

