Well, I’ve already answered the related question What do you know about Greek speaking Muslims (e.g. those in Hamidiyah, Syria)? I was tempted to merge the two questions, but the focus on Al-Hamidiyah is useful, because they’ve been so prominent in Greek media.
Outside of Al-Hamidiyah: I know that some Muslims in Greece that were subject to the population exchanges were neither linguistically nor ethnically Greek (notably in Macedonia), whereas others were both (notably in Crete, where up to half the population was Muslim in 1800). I know that the version of Greek they spoke had Arabic and Turkish words in it, just as the version of Greek that Jews spoke had Hebrew words in it, reflecting their different cultural orientation. I know there’s some Arabic-script literature by Greek Muslims, as you’ll find by googling “Greek Aljamiado”; unsurprisingly, Christian Greeks have not paid this much attention until very recently.
I know that Greek Muslims were more liberal in their Islam than those of the Middle East, with much greater Bektashi Order influence. Something they had in common with Muslim Albanians, in fact.
And I know that I find the story Ioannis Kondylakis: How the village turned Christian more poignant than its author probably did…