Hi thanks for the replies.
Yes it's a coating on the outside of the windshield. I believe the installer got careless and left the prints on the inside of the windshield. I've had those fingerprints since I bought the car, I only figured it out after my last visit to the dealership. They left a sticker that said the coating will need to be re-applied after 15,000 miles.
The "quality" or brand is unknown, but I did try several all-purpose cleaners and one of those "magic" eraser sponges. I will try a 50/50 IPA mix next time. Very annoying because the prints show up when the windows get foggy, so it's hard to show the dealership anything is there at all.