mine shreds her pee pads too and fluffs it around the house. there were a couple of times where she flipped the pad over and used it on that side. and i, not noticing, picked it up and the pee dripped off onto the carpet.
i want to get into washable pee pads, but so far, what i found useful (i kind of want to use up all these disposable pads first) is bitter apple spray. i spray it around the edges and around the pee pad and she rarely shreds it.
i used to think she wouldn't go to it because of the bitter apple, but i took a pee stained napkin and put it in the middle and now she goes on it, with less shredding. she still does it sometimes. it's just less.