What should I do about this tooth in the very back?

Around May of this year, I started noticing that my breath was consistently smelling bad. Then I saw the wisdom tooth coming in and determined that it was the cause of the odor.

It's already erupted out of the gum, and it doesn't hurt at all. There's no pressure or discomfort or anything like that. The back of the tooth is still partially covered, however. The only thing with it is that it smells. Is there anything I can do to permanently get rid of the smell, besides removing the tooth? I don't have health insurance so I'm hesitant to undergo a surgery.