I've got one to. My mystery animal finally showed itself now that it has gotten cooler and I have been out there closer to dark. Would you let one stick around for a while if it was living in a big pile of dirt instead of the dam? It sure is cleaning up some of my pond vegetation problems, and since it is not living in the dam. . . Unless they make multiple dens? I think it took to the pile instead of the dam because of the lack of roots in the pile versus my extremely brushy dam. I was thinking I could let it stick around until early summer, or later if it does not breed.
Normally I would advise to kill any invasive alien critter, but it's too late for nutria. 1 or a dozen won't make any difference. If they put a dent in your weeds and don't dig up your banks and dam, may as well get some use out of them.
I'm surprised that the slow moving nutria haven't developed many natural enemies. Down south, alligators eat the big ones and snakes eat the young.