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Greece invaded Turkey

Would you deny Spain it's Reconquista?
Ancient Greek civilisation vs. Turkish tribe culture latter descent.
Can you really invade realms rightfully yours?
The Byzantine Empire held Arabs in check for several hundred years, more than could be said about Spain. The weakening of it by the 4th crusade evidently took it's toll.
The Rascian Emperor wanted undertake a crusade against the Ottomans, but the attempt was obstructed by the Catholic Hungarians.
Given the result of the battle 1389, the Turkish Sultan was slain, a crusade with much more combatants and earlier undertaking would most probably have been successful.
The Ottomans would not have gained the strength they had when they met the Serb forces 1389.

the expulsion of the Anatolian Greeks bears a lot of semblance to the Israeli expulsion of the Palestinians Arabs.

Now, that is a strange perception...

His being primarily responsible for the Turkish victory at Gallipoli

Not much would have happen with the Turkish army if it wasn't for Liman von Sanders.
He accepted command of the Turkish First Army in the Bosporus. Later he was placed at the head of the Fifth Army sited at Gallipoli, and is widely credited with overseeing the failure of the Allied army's attempt to land there.
He was unsuccessful in his attempts to prevent the Armenian massacres or to persuade War Minister Enver Pasha to cease military operations in the Caucasus in 1916.

>>Can you really invade realms rightfully yours?

To answer your question involves the definition of the term "rightfully," which is perhaps the biggest can of worms of history.

Does the US have a "right" to the territory it now occupies, most of which was acquired by conquest from the original inhabitants, in a way not terribly dissimilar from how the Turks gained control of Asia Minor?

On what rationale did the 20th century Kingdom of Greece hold title to Anatolia, last controlled by Christians of the Eastern Roman Empire 700 or 800 years earlier? Are you aware that it is highly debatable whether there is much genetic connection from the ancient Hellenes to the modern Greeks? Most of the modern inhabitants of Turkey are probably as genetically "Greek" as the inhabitants of modern Greece.

Do Moslems have a legitimate right to live anywhere on Earth, in your eyes?

BTW, have you ever read about the atrocities committed by the advancing (and retreating) Greek Army in Anatolia?

Can you really invade realms rightfully yours?

The Selcuk Turks had occupied most of Anatolia since the 12th century.

By your reasoning, North America rightfully belongs to the Native Indians
since European invaders arrived here much later than the Turks to Anatolia.