Just don't handle them, it's believed that they carry leprosy.

True they do carry it

If I could trap the darn critters they would be dead critters! The corner of my house is going to fall into the hole they keep digging there.
I've set a trap but only caught opossums.

You should guide them into traps using boards like a funnel effect set up near their pathways or right outside the hole. I caught one each in two traps in one night this way.

Agree with Flatwoods_farm on the method. My neighbor paid a "critter getter" to set up a trap and remove an armadillo. The trapper did not put any food at all in the trap. He brought some small 3-foot sections of garden fencing with stakes along the bottom that you just push into the ground. He set up two almost-parallel rows of fence, funnel-shaped, starting at the hole and ending at the entry to the cage. It worked. No bait in the trap whatsoever. Apparently the armadillo, who has poor eyesight, just bumps along the edge of the fencing until they stumble into the cage.

Carol in Jacksonville