Window screens do a good job of letting the cool breeze in and keeping the insects out—that is, until your cat starts shredding them with his claws. Repairing screens again and again after your cat shreds them can get costly. It is far easier to prevent the cat from shredding the screen in the first place, and you can accomplish that with one or more of these methods.
Place aluminum foil on the window sill.
Many cats do not like the feeling of crinkly aluminum foil under their paws. If you unroll a few sheets and place them on the window sill, your cat will stop jumping up there. Once the habit is broken (wait at least a week), you can remove the foil and the cat will probably stay down. You may need to put the foil back from time to time as a little reminder.
Put pull-out screens in front of your permanent ones.
If your cat is not deterred by aluminum foil, then try purchasing a few little pull-out screens. These sit in your window sill in front of your regular screens so that when your cat scratches, he scratches the pull-out screens instead of the regular, full-size ones. Since the pull-out screens are pretty cheap to replace, this option should save you money in the long run, even though you'll eventually have to replace those little pull-out screens too.
Clip your cat's nails.
This method is best combined with one of the two methods above, since it won't keep your cat from scratching entirely, but will minimize the damage when he happens to get a scratch in. You can use regular, human nail clippers to cut each of your cat's nails. Make sure you only cut off the tips; don't cut to the quick, or the vein that is found in the portion of the nail closest to the toe. If you're not confident clipping your cat's nails on your own, ask your vet to do it for you.
Spray the screen with repelling pheromones.
Most pet stores sell pheromone sprays that will keep cats away from items they are sprayed on. Usually, these products do not have a scent that is discernible to humans. Spraying one on the screens and the surrounding window sill may help keep your cat away. However, some cats are more sensitive to these sprays that others, so you might need to use this method in conjunction with the others for it to yield the best effects.
If you need to have your screens repaired, contact a representative from a company like Roys Screen Service.