What do I do if I find a big fat scratch the day after installing the windows?

Silly question: are you sure it's really a scratch? Because we had that too. We also got these "scratches" on one of our windows after the windows were installed – 3 of them! I immediately panicked. It looked exactly like yours. It looked like a scratch (you could actually feel it when you ran your finger over it), it looked...just like yours in the picture. I wiped it off with a rag, hoping it was just dirt..... Nothing happened. Then my husband wiped it with a damp rag, with a little more force and a little longer than I did, and lo and behold: the "scratches" were gone. It was gone. Completely unnoticeable, as if nothing had happened. No change in the structure of the film, no bumps or depressions where the "scratch" was, no difference in color from the rest of the window. You can't tell there was anything there anymore. I have no idea what it ended up being, but it wasn't a scratch. I suspect it might have been some glue residue or something very stubborn, I don't know! Either way, there isn't and hasn't been anything interesting there. Even now, months later. That doesn't mean it will be exactly the same for you. But look again carefully. If in doubt, report it to the GU before you mess something up by scrubbing it off yourself (in our case it was more luck than common sense :D).

The scratch can only be repaired with colored wax or lacquer pencil. But it won't be invisible.

Honestly, leave it as it is and apply paint! We went to a specialized company, a piece of the frame where there was a scratch was re-covered with film, but unfortunately, the glue loosened and the film was covered with bubbles.