I am not sure if any measures are taken to prevent cross-contamination. I do not have celiac disease, just an intolerance to gluten, so I do not need to worry about cross-contamination as much. To make my burger gluten free I always order it without a bun wrapped in lettuce.
I do know that they have an area on their website listing all their food items and what allergens (if any) are in them.
— Some
— Excellent