I think it comes from Smyrni and the old Greek cities in the coast of Asia Minor, who were for a while a part of Turkey (until the Greeks there were slaughtered like lambs).
Anyway we have lots of Turkish loan words in the Greek language. To the best of my ability to transliterate these examples in latin characters: ati, passoumi, briki (ibrik, I think), kazani, charatsi, tsoglani, bairaki, chatiri, dounias, giouroussi, boulouki, dragoumanos, doulapi, and derti, of course, etc. As you can probably tell, we always tend to add an "-i" at the end.
We also say "halali" and "harami", which we clearly took from the Turkish.
And of course, Tsantirimin Oustoune, and other all time greatest hits:
