smell is rot and mold
PHEW! I know what you are referring to. Unfortunatly, there is bacteria at work in the mat, eating away at the residuals. Your best bet is to use a mild solution of carpet cleaner and warm water on the carpeting , getting it nice and wet and cleaning it well. (scrub gently, don't pull up the fibers and be extra cautious around the logo). Then dry it by sopping up all the water and put it in a dry warm area - direct sunlight can cause fading. Do not put back in the car until it is totally dry. I would recommend cleaning the carpet below also.
Hope this helps, the alternatives will only mask the odor and the destruction will continue.