Letitgo is Prince a video made to promote the single from the Come album. While Prince/ did make videos for Come, Race, Pheromone, Loose! and Papa (included on The Beautiful Experience TV-special), these songs were not released as singles. He was not actively working with Warner Bros. to promote the album and thus a video for Letitgo was made (much like Pink Cashmere) using footage from the 3 Chains O’ Gold home video that was released on the same day as the album in the USA.
Footage selected from the 3 Chains O’ Gold are mainly from The Continental and The Max videos. The last two minutes or so of the video are the full ending of the 'soap opera' with Prince having a meeting to sign a contract. Of note, this scene is played during the closing credits of 3 Chains O’ Gold while Letitgo contains the original footage, not obstructed by credits.