If you have skunks digging in the lawn, they are going for grubs, get rid of the gurbs and the skunks stop digging. There is a natural product that you can apply that kills the grubs over a year or so, or there are some pretty nasty pesticides that will do them in quick.
I was told that as well . . . not a big fan of putting chemicals on my lawn though . . . plus the fella who told me about it said they are most effective early in the season vs. now.