That's strange! I have a face full of piercings and the only one I ever have to remove is my tongue. You'd think it would be pretty obvious that you don't have teeth in your nose or ears! Anyway, since the retainers are made of plastic, that should not interfere with the x-ray, so I'd do that!
It depends on the type of x ray equipment they're using. If they tell you to remove it, do so. Use a plastic retainer until you get home. You can't ignore their instructions, because if anything goes wrong later, you wouldn't have a leg to stand on, legally.