The neighbor probably thinks it is your armadillo, Jean.
They will quit digging once they finish off all the grubs in your lawn, of course. Maybe never??
Ann, I'd check your county ordinance about relocating wildlife. Down here it is illegal with a $500 fine if you are caught with a wild animal in a trap in your car. We can trap nuisance wildlife, but then we must call Animal Control who will come and collect the critter, and charge you $20.