Skunks are tearing up a lot of lawns in west Michigan right now in search of food. The most likely item they are searching for is grubs. Even if you kill the grubs, skunks will continue to dig for another week or two. Your best option is to trap them and relocate them.
Grubs are already mature and feeding on the grass. The deep snow acted as an insulating blanket to keep the ground from freezing. That means that grubs never went that deep and are already at the surface and feeding.