how can i get my newly adopted cat to stop climbing the window screens?

Cat furniture, cat trees and cat condos are great additions to a cat lover's home, as they provide hours of good fun for the feline companions and keep your own furniture intact.
Cat scratching is a perfectly normal behavior for a cat, and if your cat is scratching a chair or your favorite couch, then you just need to somehow re-direct his or her scratching to other, more appropriate objects.
The consensus from the various Societies for the Prevention of Cruelty to Animals (SPCA) is that de-clawing is cruel and unnecessary. I can only agree with this conclusion. However, if you feel that you must either declaw your cat or give her up, we would rather see your cat stay in her home and be your lifelong companion. I only ask that you do not make this decision lightly and just be absolutely sure that you will not change your mind later about keeping your indoor cat once you have it declawed.
You can use nail caps for the cat's front paws as an alternative to getting the cat de-clawed. This is a much more humane choice and it does work to protect the furniture. Just make sure you do not use nail caps on a cat that goes outside, as it will have no defense.
Most pet shops offer different selections of cat scratch posts from which to choose. Some have carpet or rug material on wooden posts and bases. Others are made of rope which is wrapped around the post or pole.
Then there are cat towers and cat trees which are great for the cat to climb and play besides being there for scratching purposes.
Other people like to design their own and make them themselves. This is another option for you as well. Besides going to your local pet store, you can look online for these different cat trees, towers and scratch posts.
One thing that can work well if your cat is still scratching the furniture is to spray some citrus oil on the chair or the couch that they are attacking. This is a good deterrent that usually works quite effectively.