If its anything like wallpaper use a spray bottle with warm water and a puddy knife. You might also try wallpaper remover solution found at paint stores.
Lynn
Present Layout progress
http://cs.trains.com/mrr/f/11/p/290127/3372174.aspx#3372174
Sand it off (it's only paper, you should go through it fairly fast) or, if it's flat enough, just put the new picture over top if that's an option. Depends on relative sizes and shapes, of course.
Heck I'd just place a thin new layer of masonite over it and put the new backdrop onto that...lot less head aches.
Have fun with your trains
You might try steaming and a putty knife. Do a little at a time. Good luck!