Do you know why this is happening? Can you post some pics?, if there is swelling, there may be a possible infection which means a vet visit is in order.
It looks like your screen could be causing the issue. From the pics it seems like the holes might be big enough for his nails to get caught in and then get ripped out. I cannot see his feet too good from the pics and can see some swelling in the one I think. If the swelling does not go away and they turn reddish in color I would get him to a vet.