May depend on the country. I called the phone support, they understood the problem and pointed me to the local Nokia shop. There is one in the town where I live. I went there, and despite the fact that he never saw such a thing, he said: yes, I'll handle that etc.
I just did not follow through for the simple reason that my device would have to be sent to a central place. Since it's only a minor annoyance with the screen, I did not want to not have my 770 for a while, so I'll wait some more weeks. In particular since I assume that they are still on short suppy, and I don't know if repair infrastructure is already in place.

It does not matter that it had been bought online, they said.