personally I wouldn't lift it. when you say damaged by cats in what way. perhaps a gentle prune to improve the overall shape would benefit the plant. if the cat is still around, the problems it causes will still be there.

The cat has pounced on it, several times. My thinking is it was trying to catch a mouse or something . Damaged the front of the plant severely.

When I've cut hebes back severely they have recovered.
I would try cutting back to below the damaged portions as you have nothing to lose. And perhaps keep sprinkling some ordinary pepper round the plant to deter the cat from making a habit of it.

Naughty cat wants a slap on its bottom, I would also trim said shrub, our Toffee is a beggar for jumping on one of mine, I think its because it grows near a gravel bed in which a lot of spiders live....