I imagine the cardboard boredom breaker is better for her to nom than the cat bed :-O
That's nothing... you should see what she's done to the sofa!
Others have said cardboard is bad and that store bought toys should be avoided... while I agree to a point, she's chewing anything and everything so, as you said, cardboard has to be better than plastic, fabric and treated/varnished/painted wood.
I can get black produce boxes from my local supermarket. I chose them over other cardboard boxes as they're very strong and can support her weight if she sits on it. I don't know what ink is used colour them but I assume it's the same as - or at least as safe as - newspaper ink. I mixed up some flour, cornflour and water into a paste and used it to glue alfalfa dust and bits to it.
She doesn't like it as much as the store bought boredom breaker carrot house but then it hasn't got carrot bits stuck to it. It was a first attempt just to see if the flour-glue would be sufficient to hold the hay, which it was.
I've found a 500g bag of "Organic Dried Carrots 500g" online for £5... the dried makes me assume it's not dehydrated which I read somewhere makes a difference although how much of a difference I'm unsure.
I was thinking of making a cardboard bunny maze, perhaps with a couple of levels and sticking different dried food to the roofs - dried carrot and perhaps other bunny safe vegetables, crunched up pellets, hay, maybe a small rabbit muesli patch, a dried salad/herb patch.... but was dissuaded when I asked in the Diet & Digestion forum so I'll leave it for a while.
EDIT: I've also asked, both here and on reddit, if there's a safer and (although not as importantly) stronger glue than flour mix... but didn't get any replies other than that flour isn't good for bunny.
I know that much, but the amounts are very small and, if the glue was stronger, then it'd be even harder for bunny to consume. If respectable pet shops are selling boredom breakers from reputed manufacturers they are clearly using a rabbit safe glue which *is* stronger... so is it PVA? I used to eat PVA all the time when I was in first school... it's non toxic for humans, so what about rabbits?
I haven't been able to find a solid answer, only opinions... the obvious one being "if you're not sure, don't do it".