If your chin is eating the cardboard, i would remove it. Consistently eating it can lead to impaction. There are alternatives- use safe wood for chew toys and fleece covered or PVC tunnels if you want them to have a place in the cage to hide/play. Just make sure that your chin doesn't chew those as well.
I use those "Chube" cardboard tunnels in the play area where I am always there to supervise.