The jurisdiction is not simply the territory of the Greek state, and the exceptions are deliberate rather than accidental.
The dioceses of Macedonia, Epirus, Thrace and the northern Aegean islands, acquired by Greece in 1912 and 1913, are the New Lands. They remain canonically part of the Ecumenical Patriarchate and are administered by the Church of Greece under a patriarchal act of 1928, so their bishops sit in the Greek synod while commemorating the Patriarch of Constantinople. The arrangement is workable and has produced periodic friction over who appoints them.
Crete has its own semi-autonomous church under Constantinople, with its own synod and archbishop. The Dodecanese, Italian-held until 1947, is directly under Constantinople. Mount Athos is under Constantinople as well and holds a self-governing status written into the Greek constitution.
Within the country the church is recognised as the prevailing religion. Clergy salaries are paid from public funds, religious instruction is part of the school curriculum, and the resulting questions about the place of the church in a plural state are argued in parliament rather than in synod. A revision of the constitutional settlement was proposed and not carried in 2018 and 2019, which is a fair indication of how difficult the question is.