Grey market can mean several things. Big Grey market outfits like Jomashop get all their pieces directly from the manufacturer. Usually it's overstocks or discontinued models. Those watches are factory fresh with all boxes and papers and tags intact. Usually there is no factory warranty card, they remove it and replace it with theirs. Some Grey Market outfits deal with watch stores and take whatever they can't sell. it could be a demonstrator or a loaner or a watch sitting in a hot display for a couple of years. Those may come with papers or may not and will once again have a dealer warranty. Some Grey market outfits grind the serial numbers off and those you should never buy because the manufacturer will never repair that watch even if you pay full service costs yourself.

You say your authorized dealer will take care of it. He probably has his own service.Call Tudor and ask if they will honor the warranty at their factory service center and that is how you will know. If they say yes then you know it is not Grey Market. If they say no then you know it is.

As I recall Chrono24 acts more like an agent to sell used watches. They may or may not sell new pieces but from what you describe it sounds Grey market and the shop in Athens just had this excess inventory.