Any of the hamburgers hold the ketchup, hold the bun are fine for low-carbing. A side salad with their ranch dressing rounds out a meal.
So long as you're just lowering your carbs, you could have the grilled chicken (those being extremely strict would probably avoid them... they're injected with a sugary marinade) sandwich without a bun or the grilled chicken salad.
Mayo is perfectly "legal", so is mustard. Pickles & onions are OK. Cheese is fine, too.
If you're there for breakfast, sausage or bacon and eggs are your best choices. If you have to, get one of the breakfast sandwiches, hold the bun.
You don't need any carbs from white flour buns or fries. All the carbs you need should come from vegetables, low-glycemic fruits, whole grains (including 100% whole wheat, flax, rolled oats...), nuts and dairy products.
Congratulations on taking care of your health while you're young!