How long have you lived there? If you have been there 5 years in many states you don't have to pay for carpet damage because there is an assumption that normal wear and tear has made it depreciate beyond value so it isn't part of the security deposit or cleaning deposit.
Assuming you are stuck, don't repair the ruined area until you are ready to move, because kitty might ruin your repairs too! You could try putting scratch pads over those areas, but that didn't work with my kitties, they wanted real carpet to ruin. Samturtle has the best solution if you can get some scraps. Another trick is to swap carpet out of a closet. Find a remnant or carpet on the roll that looks as much like the original carpet as possible, especially thickness and texture. Take a one foot section out of the deepest back corner of the closet that is the hardest to see, use that chunk to fix the kitty damage, and replace the square in the closet with a piece of remnant. If you cant match it well enough, you might be able to recarpet the entire closet with the new stuff, and save what you took out to fix any future damage from kitty. Places like home depot sell carpet. A one foot piece of a 12 foot roll is 12 square feet, or less then 2 square yards. Even 20 dollars a square yard that isnt too bad. It is sure worth a try. Good luck. | 
