There's probably not much you can do at this point beyond writing a letter and hoping for the best. My advice would be to do that with the expectation that it may or may not get to the right people, and then forget about it and move on. Don't let it continue to take up real estate in your head. As others have already said, these issues are best dealt with at the time, and with the manager directly in charge of the person. Anything else can lead to it getting lost in the shuffle, and it becoming a "he said / she said" situation where nobody can really say what actually happened, and thus nothing gets done about it.

As to poor service at an airport, coincidentally the only time I had an issue similar to yours was at LHR - in my case, at a Duty Free shop in Terminal 2. The behavior of the cashier was atrocious, to the point that it was almost comical, and I had done nothing wrong to prompt such behavior. I just kind of laughed it off, until I met up with my friend a few minutes later and he said "You should have seen how my cashier acted!" We had both had the same experience just minutes apart, so we knew it wasn't us. We tracked down the manager on duty, explained what happened, and identified the offending staffmember. We made it clear that we didn't want anything from her and weren't expecting anything, but that if we were the manager, we'd want to know about this employee, so that's why we're telling her. I felt that was the best way to handle it, and the most likely to result in the manager doing something about it. Anyone in public-facing role has to deal with a certain percentage of people that get unreasonably upset about things and demand compensation of some kind, and I didn't want to be dismissed as one of those. After informing the manager, I felt the issue closed as far as I was concerned. Whether the manager did anything about it is up to them, and I hadn't thought about it again until just now.