I took a handful of clues from various isolated incidents in Skin Game. One, when Harry realized that he hadn't told Gray where Michael lived. Two, when Harry noticed that Gray was paying very close attention to what Michael was saying--was that about the redemptive aspects of faith? I'd have to check. Then, when Uriel said that Gray attempting to enter the Carpenter yard would have been "awkward". Oh, and also, because Michael knew right away that Gray was a very bad person.
Well, Gray is a monster for hire. It would hardly surprise me if at some point he took a contract on Michael, headed for the Carpenter House--and got his...er, tail handed to him.
Faced with the possibility of eternal damnation for his actions, he was told by a divine entity (I don't think that Uriel is the only archangel familiar with the Carpenter House) that he needed to atone for his lifetime of evil acts. Do a good deed every year, every month, every week, whatever, to counteract all of the bad things he's done over the centuries.
In other words, Gray has a temporary lease on remaining on the mortal plane. That's the key point.
The dollar merely reflects that it has to be a contract of exchange, where he's sacrificing money--rather than simply helping little old ladies across the street.
Perhaps he was even told not to come back to Michael's house (or similar divinely protected places) until his Rent was in a positive balance.
All of that is a WAG. Lots of unknowable variables in there. But I suspect that I got the general shape of it correctly.