The squirrel that hangs at my house is Bucky....
. He runs from the palm tree in front, across the roof, jumps on to the cage and heads down to the ground. Some days he jumps from the cage to a palm tree near the cage. So far, and it's been a few years, the squirrels haven't damaged the screens. About a year and a half ago, there was a Mrs. Bucky and 4 little ones. I'm more concerned about the wee beasties getting into the attic, but so far, they haven't. You could get a humane trap, capture them and then release them somewhere other than your yard, but my feeling is the squirrel realtor would just get in touch with squirrels on the waiting list looking for new digs.