When we were on the Magic in November, they were giving people the option of tortilla or pita. The pita were in unmarked/generic bags so I didn't see any label on them or anything.
You may find this helpful: one thing I love to do is get some Shwarma (just the meat) and then go over to Daisy's Delights and have them add salad/other toppings to the meal. Its a great way to enjoy shwarma without the extra carbs from the pita. Usually, I just get two separate dishes and combine them myself and it works wonderfully.