Colorado

it does appear that the co-worker finally found an issue to complain about. The co-worker couldn't complain about the wallpaper showing a picture of her wife since it would be discriminatory to remove that picture, but allow other employees to have personal pictures as wallpaper.

Whether she has grounds to claim that she was in a hostile work environment is best left to attorneys the civil justice system. Her case would be stronger if she did try to settle it in mediation with the hospital. I do expect that the hospital will implement stronger policies not allowing any type of wallpaper photos or screensavers to be on their computer system because of the exposure to liability and media publicity.