How do you "get rid of" a stain that even bleach won't disguise?

The shirt is something like 65% polyester and 35% rayon (or something). I have no idea how old the stain is or what it is. I got the shirt ridiculously cheap at a thrift store, thinking I could get rid of the stains, but i seem to have proven myself wrong. It's a faint (but noticeable) grayish stain. Help!