The last time I went here they told me that they don't have anything they can say is gluten free for sure. This was only 2 months ago.
Their fries at the kop location are NOT gf. I just called them a moment ago to confirm this with a manager. I was hoping to try this place out several months ago, but their fryer isn't dedicated and they do fry foods with gluten in them making all their fries contaminated. Though some locations do have dedicated fryers, this one doesn't and I suppose its a lesson in asking about the fryer situation at each location you visit since it will vary.
I am about to be in NY chaperoning a school field trip, and I called them to verify gluten information. They were very knowledgeable. They can do all the burgers without the bun, but the shroom burger is covered in bread crumbs, so it cannot be made gluten free. The fries are gluten free, but they are fried in the same fryer as the shroom burger, so there is cross-contamination, so if you are sensitive, AVOID! Their custard items and drinks are gluten free, but some of their mix-in items are not gluten free. They are clearly marked on their allergen chart, though. I give three stars because they were knowledgeable and try to accommodate, but they don't have gf vegetarian options or fries that are safe.