Cats like to scratch things to sharpen their claws, including pet toys and scratching posts if you're lucky, and furniture such as couches if you're not. This can leave snags, tears and small thread loops on the couch from where the cat pulled the thread or fabric out of the couch during scratching. While it is not possible to restore the surface of the couch entirely to its previous appearance, it is possible to make some repairs to the area where the cat has scratched.
Snip away the threads pulled out of the fabric carefully with very sharp, small scissors to. Snip the thread as close to the surface of the fabric as possible without cutting the fabric itself.
Match thread to the couch fabric as closely as possible. Using a small-gauge sewing needle and the thread, sew up any holes in the fabric. Tie together the ends of the thread and create a small knot.
Use a fabric patch in the same color as the couch fabric to repair large holes in the couch fabric. Alternatively, use a small patch of fabric from the bottom rear of the couch or an arm cover to cut a small fabric patch and sew over the hole, using the matching thread.
Place a large piece of sticky adhesive tape over the repaired portion of the couch to dissuade the cat from causing further damage.