From Catspaw Dynamics: In 1963, Robert K. Abbett was commissioned by Ballantine Books to paint the covers for Edgar Rice Burroughs’ Barsoom series. 1965 saw the addition of John Carter of Mars as the 11th book, and Thuvia received a new cover in 1969. Abbett would also paint a Tarzan series of covers.
For the two different editions of Thuvia, I’ve read two stories. The first is that Ballantine accidentally published one of Abbett’s roughs (Thuvia with the banth), and they didn’t correct it until later. The second story is that John Carter helping Thuvia out of the flier was too risque for 1963, what with the skimpy bikini, and going with the more chaste mini-skirt was the compromise until society caught up. I’m sure someone more knowledgable than myself will bring some clarity to this.