My parents in IN have quite a time with muskrats destroying seawalls around the lake...then you get to watch the yard decay into the water. Dad has mentioned attempts to relocate them without success - they're always back. Or some are back - we don't exactly check IDs.
I was a teenager at a high point in the market, so did a good bit of trapping muskrats. I can highly recommend Conibear traps (over legholds or snares) as easy, quick, clean (instant kill, no blood, etc). Set right in the mouth of the run, chained to a stick a little off to one side. One of these will clean out a den in a week or so. My understanding is there's no season on muskrats now, like there used to be. That is, open season all the time.