Why was Happy and Carla affected by Azuma's take over of Tenrou Islands magic?
While I never can't remember see Carla's guild mark, Happy have it behind his back, Picture below is from Galuna Island arc when Gray met Lyon on Curse Island, they (local villager) ask for Natsu, Gray, Lucy, and Happy mark to prove it if they are Fairy Tail's Mage.



So if happy has it, it not weird that Carla also has it. But she usually wearing full clothes so maybe it's hidden behind her cloth