Sometimes you're better off. In that situation if they got a large enough piece. Ide cut it all out. Damage is already out beyond the door frame. And i can see the seam is in between the door stops instead of under tge door. So you'd have a rectangle patch one way or the other. At least with cutting out that entire area the seams will die in to the outer door frame and the walls. 2 seams Easy peasy. If they dont like the new to old difference i give them a replacement price leaving the ball in their court to decide.Don’t cut out so big of a piece. Just row cut the carpet. Take your remnant piece dry fit it in there underneath cut along the row trim the fat off dry fit seam tape iron tractor put a tray on the seams done.
Is that pet damage?