I'd suggest baking soda or activated charcoal, closed up in a container (like a big Rubbermaid tub) with the fabric. You may need to replace it more than once, but it should help.
I've also heard that crumpled-up newspaper can absorb smells. It's cheap and worth a try.
Could you lay the brights out in the sun face-down? A big patch of clean, dry grass wouldn't hurt anything, and if the print is facing down it shouldn't fade.