https://wwi.lib.byu.edu/index.php/Treaty_of_Lausanne

Except where a provision to the contrary is contained in the present Treaty, the islands situated at less than three miles from the Asiatic coast remain under Turkish sovereignty.

The islands are more than 3 miles from the Asiatic coast, (Turkey/Turkieye) so it's not Turkish isles, according to the official treaty. 

