How to Protect Screens from Cats
To protect your screens from cats, apply an herbal scratch repellent spray to the area once a day until the cat no longer goes to the window. If that doesn't work, attach chicken wire to the side of the screen where the cat usually scratches. In addition, you can spray your cat with a spray bottle or a water gun every time it starts to scratch the screen to discourage it.
Make sure your cat has a scratching post. It will be much easier to keep your cat from scratching the screens if it has another place to go when it needs to sharpen its claws. You can purchase a scratching post from a pet supply store or you can make your own from particle board, a post, and carpet or rope. Indoor cats don't have as many options for wearing down their claws, and they can become painfully overgrown. If your cat is scratching a screen, use vertical scratching posts rather than horizontal ones. Trim your cat’s nails regularly. This won't completely prevent your cat from clawing at your screen, but it can help deter it. If your cat has shorter, dull claws, it won't be able to get as good a grip on the screen, helping discourage it from climbing or scratching the screen. In addition to helping to protect your screen, trimming your cat's claws will help keep your cat comfortable. Take care not to cut your cat's claws down into the quick. This can lead to pain, bleeding, and sometimes even infection. If your cat resists having its nails trimmed, take it to a professional groomer to avoid either yourself or the animal from being injured. Use a spray bottle to discourage your cat from scratching the screens. Every time you see your cat getting near the screens, spray it with a little water. This won't hurt your cat, and it will send the message that it should stay away from the screen.  A common household spray bottle will work, but if it previously held a chemical cleaner, make sure you wash the bottle out completely. You can also use a water gun. You'll get a more targeted spray, plus it will help relieve some of the frustration caused by your cat scratching your screens! Apply strips of double-sided tape to the windows for a quick fix. Cats can't stand the feeling of anything sticky on their paws. If you lay strips of double-sided tape across your screen, your cat may begin to associate the screen with that sensation and leave it alone. You can use regular double-sided tape, or you can purchase one that's specifically designed as a cat deterrent. Spray a scratch deterrent onto the area to repel the cat. Most spray-on scratch deterrents are made from herbs which either smell pleasant or are odorless to humans, but cats can't stand the smell. You may have to reapply the spray each day in order for it to continue to be effective. You can find scratch deterrent at most pet supply stores, or you can order it online. Use a motion-sensor can of compressed air that spritzes your cat when they approach the screen. These can be purchased at pet stores or online. Install chicken wire over your window to discourage climbing. Using a heavy-duty staple gun, attach the mesh to the wooden frame around your screen. Most cats don't like the feeling of wire mesh against their paws, so this can be an effective deterrent against the cat scratching or climbing your screen. Chicken wire is commonly used in gardens and other outdoor spaces as a safe way to discourage cats from entering certain areas. If your cat scratches the screen from the inside, place the mesh between the screen and the glass. If the cat climbs the screen from outside, nail the chicken wire to the outside of the window. Replace your screen with a pet-proof screen if nothing else works. If you just can't keep your cat from tearing up your screen, you can purchase a heavy-duty screen with tear-resistant mesh. You can find heavy-duty screening at most hardware stores. Use duct tape, screws, or nails, to reinforce your screens from the outside. Cats love to rub against screens, whether it's to leave their scent or as a way to get closer to the outdoors. Unfortunately, if your screen isn't sturdy, your cat can push right through and escape. If you're concerned that the problem is the frame that holds the screen in place, anchor it more securely to the window frame by driving in screws or nails. If you need a quick fix, lay strips of duct tape around the outside of the window until you can come up with a more permanent solution. Install secure latches on the screens. If your screen opens, your cat may have an easier time pushing through it. Childproofing window latches are a great option to make your screen more secure, and they are usually fast and easy to install. Look for childproofing window latches at a home improvement store, or search for them online. Replace your screen with childproof window mesh to keep cats in. If you're worried that your existing screen isn't strong enough to hold your cat in, you can purchase a heavy-duty screen with tear-resistant mesh at most hardware stores. This is a great option if your cat hangs out near a window that's especially high. 
Make sure your cat has a scratching post. Trim your cat’s nails regularly. Use a spray bottle to discourage your cat from scratching the screens. Apply strips of double-sided tape to the windows for a quick fix. Spray a scratch deterrent onto the area to repel the cat. Install chicken wire over your window to discourage climbing. Replace your screen with a pet-proof screen if nothing else works. Use duct tape, screws, or nails, to reinforce your screens from the outside. Install secure latches on the screens. Replace your screen with childproof window mesh to keep cats in. 