Ownership of that zone is related to that of the island of Kastellorizo (Meis in Turkish) according to international maritime law conventions. A few hundred Greeks live there and the island falls administratively under the larger Greek island of Rhodes, but is claimed by Turkey. According to Turkey, it’s an idiot that an island two kilometers off the coast and 580 kilometers from Athens would belong to Greece.
Earlier, Turkey had signed a controversial treaty with Ankara’s military-backed government in Libya, dividing the maritime border between them and allowing Ankara to suddenly claim much more sea area. That treaty is now being contested by Greece, but also by Cyprus, Egypt and other riparian states. However, Kastellorizo’s possession crosses out the Turkish claims.