How do I fix this?

Give the cat other options to scratch on. A cat tree, the cardboard ones etc. Reward them for using the correct ones and fix the hole the best you can. Unfortunately cats are curious critters and they will get into most things when they get bored. Play with them and give them lots of attention and hopefully the "bad behavior" will go away.

Put a rug over it or use some sort of fabric glue to fix it somehow?