I tacked up remnant carpet pieces over the molding so when my cat scratched, it did no damage.
A super-quick and cheap fix for the molding would be to smooth it a bit with fine sandpaper or steel wool and then use brown shoe polish
Aluminum foil simply taped over the spots will stop the problem. My sister's cat is doing the same thing to our house. (naughty beast.) but once I put up the aluminum foil, the cat stopped. Cats HATE the feel of the foil on their feet, so you can put this anywhere they are not supposed to scratch (but do anyway. LOL)
Also be sure you have a place where the cats are allowed to scratch. Walmart has a cardboard scratching pad with catnip in it that the cat really does like ($5). We put it on on the floor next to the aluminum covered molding.
I used to work for a vet. One of the best ways to deter a cat from scratching is to use foam double sided tape. After the habit is broken any residue can be removed with alcohol. I have even used it on couch corners. It is a guaranteed solution. Your cat will be very upset the first time it's paws stick, but won't be harmed.
I would also get glue-on covers from the vet or the internet to cap the claw tips on the cat, they look kinda cool in hot pink or whatever color you choose, and would stop future damage completely.
First you need some fine sandpaper to sand the high spots in your molding and then take some "Old English Scratch Cover" Pick out the color that most represents your molding. I use this on my old dressers, cabinets and ect. It will cover a lot and makes it look nice. This is sold in the furniture polish aisle.
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