They didn't have any gf pita on the Wonder, and they advised against the meat itself for DH. Too much cross contamination, I think. They looked sort of freaked out by the question, but after getting it myself, I understood. They pretty quickly assemble it, and everything they use (utensils, meat, every condiment) touched or almost touched the pita. I would assume the set-up is the same on both ships, and I guess it's a little impossible to have a new, uncontaminated spit of meat at the ready. If you don't have celiac and aren't sensitive to cross-contamination, I don't see why you couldn't get a bun from the burger area though, and have the meat and toppings put on that. Not the same, but maybe better than lettuce?