Yeah, I've heard groundhogs will return from a ways away and relocating is illegal.
If you don't want the pest, others probably don't want it either.
Big, nuisance pests (groundhogs, raccoons, etc.) that nobody wants around here that end up in my trap I'll take care of.
There are some cats that roam around that I hope keep the chipmunk, mice, etc. population down, so I leave them go also.
Even though the rabbits eat the wife's plants, she won't let me plunk them.