I'm having a similar problem with Mamou kneading mine. He's just started to lie down with us, and I don't want to discourage his progress, especially since I know that it means that he's happy and relaxed, but I don't want his long, large nails (he's got huge paws and nails, but because he's outside I don't want to cut his nails. He may need to defend himself against a wild animal. Not that I think that he'll let us do it.) to do any more damage.
I told Dh that we should get a 'kneading mat' for him to knead on, which we put over the quilt and such. There's no such animal, I'll just have to choose something.
As for dogs, I used to use for an old sheet. When I first got Jet, his nails were too long, and he did something similar to Charlie. I put an old sheet on top of blankets/quilts, and he could make a mess if he wanted to, but it ended the blanket/quilt damage part.
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