That very website shows it did fly over Greenland on 24 July, the date of my post.
So which version of the flight is correct? Is it the 7/24 version of the flight or is it the current version of the flight?
This really makes me question this website because it appears that the flight path changes after the plane lands. I wonder why that is?
You do understand that a Flight Number is not unique? Most flights on popular routes take place several times a week, under the same Flight Number. So you need to specify which date you are talking about for a particular Flight Number. If you think the "flight path changes after the plane lands", then you are looking at the same Flight Number on a different day.
The route will be different each day. For the North Atlantic, flights are channelled into one of 4 North Atlantic Tracks, defined by the American and European Air Traffic Agencies. Airlines submit their planned flights to the agency the day before, and the agencies select the routes based on where planes want to go, ideal Great Circle route, weather, and jet-stream activity. The Tracks go
with the jetstreams eastbound and
avoid them westbound. As the jetstreams are a natural pnenomonon, the routes vary day to day.
Aircraft aren't obliged to follow the official tracks, but it makes economic sense to do so. If you wanted, say, to fly a rigid Great Circle route eastbound then you can; your ground track will be a shorter distance, but you might be covering the ground around 25% slower than everyone else, so it will probably take longer and use more fuel. Quite often, of course, the jetstreams do come close to a Great Circle, and then you get to see Greenland.