Ernastine, you will have to remove the wallpaper then fill the scratches with spackle. Sand the spackle smooth, apply a coat of primer-sealer, then paint. This is the "short version" of the process. Your immediate problem will be to get the old paper off without damaging the drywall so much that it has to be replaced. Replacement or patching holes may actually be easier sometimes, so don't get concerned it it seems like you should do this.
Right now, you might tell us more about how the area looks. You might also start building a good scratching post. Ours is two 2x6's about 24" long screwed together on the wide sides and those are screwed to the center of a piece of 3/4" plywood from the bottom. There is a piece of 1" dowel screwed to the top to hold the string for a toy to bat. This was all made with whatever I had at the time so it's OK to improvise. Your cat needs to scratch at will stand her new post. I would say that ours loves hers but ours love getting fed, scratched and sleeping. When she got tired of being yelled at, she tried the post and that's the only place she scratches now. Good luck with this part as the walls will be easier to do than to get your cat to use only the post.
OK--let us hear about the condition of your walls.