That Girl Thang, an acoustic track, was first available for download from Prince's 3rdEyeGirl.com website on 18 February 2013, within hours of the track's recording.
It is unknown if this song was planned for inclusion on an album or any other project.
Blogger Dr. Funkenberry, reported in an online video chat that the song was written and recorded about six hours before its release; since the song was available in the early morning of 18 February 2013, this places the recording on the evening of 17 February 2013, most likely at Paisley Park Studios in Chanhassen, Minnesota.
The track appears to have been recorded in a single take with no overdubs, however, and Prince can be heard to turn off the recording machine at the end of the track, so the track could have been recorded on a mobile device from another location.
In November 2016, dancer Lala Escarzega wrote a blogpost about the song in Instragram saying "Girl Thang"- Prince gifted this song to me after a night I jokingly asked him to sing me to sleep. I had also told him his photo he sent me made me swoon & I love how he made the lyrics so personal so only he and I would "get it". He gave this song to me the very next night. There is also an instrumental of this that he gave me and I have no idea if it was ever released or not.
It appears Michael B. Nelson also wrote a string arrangement for it, and recorded with Adi Yeshaya and StringGenius.