You can try the stuff used for getting kids to stop sucking their thumbs. It comes in a nail polish tube tastes pretty bitter.
Use black pepper or cayenne pepper attached to the cardboard you used.maybe the smell might deter them.
The idea is to deter/train them to stop. So that eventually they don't even want to mess with it.
My mom used cinnamon to get one of our puppies to stop chewing on the leg of a table... She tied whole sticks to the bottom. After she did that he didn't even try it once - I think the smell alone deterred him.
Different solution for different animals.
Our dogs and one cat we ever owned did well with deflecting/ deferring behavior with toys or other items. But never items similar to the item you don't want them to stop chewing
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