Tattoos in the center of the back on women have the potential to be damaged (scarred) by bra straps rubbing on them during healing. Minimize this risk by either not wearing a bra during the healing period, or, if viable, placing some padding inbetween the bra strap and tattoo.
Bra straps can also interact negatively with surface piercings on the back as well.
The photo above shows a tattoo that was rubbed by a bra strap during healing. One reader writes to advise:
When I got my shoulder tattoo done, I wore a strapless-convertable bra and criss-crossed the straps so they weren't on the back of my shoulder at all or near my tattoo.