Someone sweated through that thing and bacteria are still finding stuff to munch onparticularly when your own sweat activates odor particles already embedded in the pack.
Still, you should be able to fix this. For starters, I’d fill a bathtub with hot water, throw in a cup of laundry detergent, and soak the thing for a day. Swish it around a few times, and to the extent that you can, wring it out once or twice and re-soak it. Then take it outside, hose it down thoroughly to remove the soap residue, and air-dry. I’d be very surprised if that doesn’t work.
But, if it doesn’t, stronger measures may be required. Repeat the bathtub procedure, but this time throw in a cup or three of Lysol All-Purpose Cleaner. Let it soak again. The Lysol should kill any bacteria hiding inside the foam backpad. You can also spray it with Febreeze, a product that I’ve found is very effective at completely eliminating odors, rather than simply masking them.
If none of those measures works, all I can say is hold your nose!