I would never wear my letters, or any of my other sorority gear, in a different color. Even if I did a patterned background, the pattern's coloring would have to be consistent with my sorority's colors.
As far as wearing the letters across the seats of pants goes, I don't think LADIES should wear any kind of writing across their behinds, period. But, that's just my old-school, Bible-belt, South Carolina upbringing, LOL.