I don't think you can re-use the original wallpaper that comes with a house. Try putting up new paper and see if the original goes into your backpack (this is what happens when you put wallpaper over wallpaper or floor over floor). If so, you can re-use it, if not, I think you're out of luck. Sorry!
If you use the Pick Up Everything button, it picks up the wallpaper as well. Of course, you have to re-place everything, but it will give you the original walls back.
You can reuse wallpaper First: go to the wall paper in your moving adding or removing thingy then go to the side where youll she wallpaper being torn off or tile press the wallpaper to remove wallpaper press tile to remove tile if you have any questions just ask because this could be confusing