How can I get my hamster to stop chewing on her cage?

I have a syrian hamster named tilly, and she chews on her cage ALL night long! It isn't a wire cage, it doesn't have the little wire bares like most. It is a habitrail hamster suite. There is a little lip on the door of the cage that she chews on. There are also the add on plastic pieces that she chews on. My parents always complain about it, and I'm also worried about Tilly. I heard that it can cause her teeth to become misaligned, and that it can also cause brain damage. I buy the wooden chewing sticks for her to chew on, but she won't use them. Any home remedies that can get her to stop? Please don't give dumb questions. I will report questions that are inappropriate. Please help! THANKS!:]