Wild theory that may lead to the discovery of one of the wallpapers
From The Lost Media Wiki
The section for the lost June wallpaper mentions how one of the characters would have been dressed as a "frog gappa" However, the text for gappa (ガッパ) Could also be read as kappa which is a mythical creature in Japan. Therefore, the June wallpaper could be one of the characters either dressed as a kappa or being a kappa.