How do I clean one of those pack and play mattresses with the cardboard type stuff on the inside?

I made a mistake and have been putting our baby in her pack and play without some kind of waterproof pad on the mattress, and now baby spit has soaked through the entire thing, including the board, and stained it. Has this happened to anyone else, and how do I clean it? Or should I just get a replacement mattress and be more careful this time? I just want to be able to use it with subsequent babies and I'm worried that the board will get all moldy or something (not sure if this would happen or not).