Wrapi, or Warpie according to its texture files, aka the Mural Monster, is a character located in the far south of the Mural Forest.
It requests a certain tune to be played. It doesn't know which, however, that information can be retrieved in one of the houses in the Barracks Settlement. Though, just guessing the tune before that will work as well.
After having played the tune, Wrapi will vomit out the Moon Glyph.
According to the Official Website, the monster is a new character, which was "dormant in Kikiyama’s imagination (and design documents)" and "has surfaced 16 years after YUME NIKKI’s original release".