Well, I think you already did the right thing, and the bank probably won't have any idea what was that payment for, anyway. If you really want to be on the safe side legaly and consciencewise, you might want to write to hospital's billing department (using registered mail or something other traceable) asking for details of that reimbursment. Now, it they still just ignore you, there's nothing you can do (and if they remember after a year that you "have their money", you have a proof that you alerted them). After all, perhaps they did overcharge you in the first place.

Otherwise, bank errors in one's favor happen only in Monopoly