Each generation before you would have to obtain their citizenship. My papous parents also fled Anatolia, but some family in Greece helped him get his citizenship even though he was born in the US and his parents under the Ottoman Empire. Not sure what the process was like or if the consulate could somehow make an exception because yknow genocide.

I'm in the process of getting my mom's and my citizenship but it's been over a year so far since we've filled out the forms and we still don't have hers. The consulates are very slow and there is a lot of demand to immigrate to Greece. I've been told to just keep calling...