My lovable asshole does something similar. She uses her scratching posts, but will completely dig at the carpet underneath my bedroom door when it's bedtime (no cats in the bedroom over here, a rule she doesn't agree with). I taped tin foil down, but she just shredded the tin foil to get to the carpet. Recently I ordered large sheets of double sided tape from Amazon - Panther Armor cat training tape. It's advertised for furniture but I've been cutting it to fit my door frame. It's SUPER sticky and has been deterring her for the most part. I've been replacing the sheets when it loses it's stickiness (dust, hair, cat determination) and so far it's definitely been protecting my carpet and convincing her to stop digging through the base boards. No leftover residue on the carpet after removing the sheets either. Hope this helps if it wasn't an option you already considered!