Can I not pay for there mistake ?

You are asking a question about life and fairness? Put yourself in the position of the other party. If something was left out of a bill you sent, perhaps by error, should they not have to pay you? My attitude is to treat everything in life with this principle: Be reasonable and responsible. Mistakes happen to everyone. When they are unintentional they are part of life so we should all understand and deal with it. If this new bill caused you inconvenience, then, perhaps you may express that and negotiate a discount if possible........... Now for the legal part: If you received a release wherein the person you paid released you from all liability and responsibility for the debt, then they cannot come after you. Otherwise, this sounds like an agreement in contract and the statute of limitations in New York is 6 years. Good luck!