I don't know the lead singer or anything about the group, but if they're suppose to be all natural, the guys did a good job of harmonizing but the girl lead singer sang almost entirely with autotune on her vocals. It may it sound too artificial or phony and killed the acapella effect.
You caught my attention because two of my favorite songs have the moon in the title, I thought that is what you're getting at. One is the Waterboys and "The Whole of the Moon" from 1985.
The Waterboys - The Whole Of The Moon (1985) - YouTube
The other song is REM "The Man on the Moon". It's a tribute to the late comedian Andy Kaufman of Taxi fame and was also the title of the movie starring Jim Carrey as Kaufman.
R.E.M. Man On the Moon - YouTube