The charcoal idea sonds like a winner...or try spraying and wiping it with Febreeze or vinegar, but I have no idea that febreeze would be bad for the mat or not? ???? Vinegar probably wouldn't hurt it.
I have one from Wal-Mart, one of the pink on one side, yellow on the other, and it stinks. It doesn't really smell rubbery, but stinky.