I hate to be the Grinch in this delightful conversation, but the way that we "solved" not having our kitty scratch at the door is this--he is not allowed to go outside. Ever. This might seem harsh or cruel, but honestly, kitties do NOT need to roam outside to be happy. As long as they have a stimulating environment indoors and can look outside, perch on window sills, etc. they are perfectly at peace.
Our veterinarian totally supports our decision to have a 100 percent indoor cat. There are just too many predators where we live (coyotes, raccoons, etc.). Car traffic is not a problem for us, but for those living in town this is also certainly a consideration. Statistics have proven that cats that stay in doors live much longer.