Can you describe your cage set up a bit more? Having bedding all over will make litter training difficult, as the rabbit will not know where the litter box is and will treat the whole cage as it’s litter box.
Wood shavings aren’t great for bunnies. Pine shavings can be dangerous (the aromatics can cause liver issues long term), and the shavings get stuck to their fur.
Pine pellets (sold as cheaply horse stall pellets or expensively as feline pine cat litter) on the other hand are safe because the way they are heat-treated removes the aromatic compounds. I use a layer of pine pellets in the litter box only, with a nice fluffy hay layer on top. You can also only hay, and make a nice fluffy layer of hay in the litter box that you dump out daily. This works great if you are able to get hay cheaply (like from a horse supply or local rabbit rescue). Another safe bedding is carefresh, but it’s more expensive. It is nice for litter training though because it is soft and fluffy, so the rabbits are encouraged to pee on it.
All of that said, nibbling a bit of newspaper is safe (avoid the glossy printed pages though). But do swap out the bedding you are using for something safer. And putting bedding only in the litter box will help a lot with litter training. 🙂
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The answers provided in this discussion are for general guideline purposes only. The information is not intended to diagnose or treat your pet. Seek the advice of your veterinarian or a qualified behaviorist.