I would check your states' list of reasons for filing a motion to vacate. In Washington State it's called RULE 60 RELIEF FROM JUDGMENT OR ORDER. Not sure if it's called differently in each state. If you can file a motion to vacate based on paid/satisfied it should state that somewhere in the list.
Note, I haven't filed a motion to vacate based on paid/satisfied myself yet, but I plan to soon. I'm just going off of what I've read in my state so far.
I would start by googling motion to vacate list or some such for your state & go from there.
