sounds like a star-nosed mole...............you have to treat your lawn for grubs and they will go somewhere else to dig. They will do even more damage searching for grubs..............they don't like mineral oil, pour down the holes and push rocks in and then dirt............trap them they are blind, they also eat worms....................they do have a new bait for them, but if you have animals you would have to push that down the hole and rock & dirt it.............they don't like vibration............going to tell you it is going to be hard to get rid of them they have babies 1 time a year unless that litter dies, they will produce another litter.