If a collection agency refuses payment is the debt considered paid in the stste of Texas?

No. Are you saying you are offering to pay the debt, all charges and fees, and the company is refusing to accept it?

Or are you making an offer for a partial payment and they are refusing?

If it's the first, simply send them certified funds in the total amount, receipt requested.

Making partial payment of $20.00 a wwek.

They don't have to take them - they can get a Judgment against you for the full amount.