How can I get proof that an agency is refusing a payment so I do not owe them anymore?

You send them a certified letter and your check. They cash it or send it back or send you a letter stating that they will not accept it.

Without knowing more of the circumstances anything else is difficult to say conclusively.

Perhaps they are refusing partial payment?
We can't say 'you don't owe anymore' based on the little info you have given.