When do gem store items, like Mount Skins, recycle again?

Well first of all, congrats on successfully raising your siege turtle! If you haven't already found it, the Siege Turtle Advent Pack is currently available, and the Kaineng Lights set contains some siege turtle skins as well. To touch on your actual question as well, returning items rotate in and out of the gem store every week, with a different category rotating each week. You can check the "What's In Stock" section of our gem store blog posts, published every Tuesday on our website. The current mount selection will rotate on May 24.