The band was named after the 1965 Roy Head and the Traits song, and had an obvious appreciation of old school and lesser-known rock, as evidenced by the two covers on the debut album (which were by James Blood Ulmer and Captain Beefheart). In addition, they were unusual from an instrument perspective, as they used the guitar almost as a bass, and a cocktail drum kit.
Treat Her Right released three albums from 1986 - 1991. I believe that only their self-titled debut LP charted (at #127). "I Think She Likes Me" did not chart on the top 100, but did hit #15 on the Mainstream Rock charts in 1988. In typical blues style, the song is based on a true story that happened to guitarist Mark Sandman in Colorado.
After the breakup of Treat Her Right, Sandman would go on to form Morphine, and would carve out a successful career playing alternative blues until his sudden death from a heart attack in 1999.