So it seems that Turkey wants to ignore Greek EEZ, which seems to be acknowleged by other neighbours including Egypt. From the limited maps showing it seems this pipeline never gets nearer to Turkey or even Northern Cyprus than to Cyprus or Greece, thus remains in their EEZ under the UN Convention on the Law of The Sea

It seems Turkey's view is that countries like Malta, Cyprus, Cuba, New Zealand etc can't have EEZs, let alone islands that are part of a country, like Shetland, Hawaii, the Aleutian islands, etc.

Now sure they can claim whatever they want, but with EU, US and UN against them it's rather moot.