In the latter part of the episode The Lost Treasure of Griffonstone, Gilda has the opportunity to save the Idol, but at the risk of losing Rainbow Dash and Pinkie Pie. In that episode, she chooses to save the two ponies, while the Idol is lost forever. But let's say that somehow Gilda is able to save both the Idol and the two ponies. I would imagine that when Gilda brings the Idol to the surface, the griffons would pledge their allegiance to Gilda and proclaim her Queen, believing her to be the spiritual successor to King Grover.

I would image that Gilda would help Griffonstone and bring it closer to Equestria. What do you all think? Let me know in the comments.