No. Get. A written agreement stating that the $225 is payment in full before paying the money. Simply sending the money with paid in full written in will not work.
There is a fair chance they will accept your settlement offer, but here is what is working against you - they have already filed a granishment with the State, and your refund may already be on "hold" because of it. So, if they have a chance to get 100% of what they say they are owed, or some lesser amount, what do you think they will take? If you have not filed your return yet, and know the refund will be little or nothing, the offer starts to look more attractive to the Plaintiff. Get a resonse from them in writing if they accept, and include the filing of a Satisfaction of Judgment as part of the deal. No need to make this into a major undertaking when the amount in quesiton is undre $500. Good luck!