This question would be more appropriate for the geneticists in /r/AskScience. But you're going to have to give a little more info about what you mean by "Greek DNA", and how one could quantify "how much" of our current DNA is "Greek". If you're talking about descendants from people living in Ancient Greece > 2000 years ago, it's likely that their genes can be found in a great deal of the population, in common with other peoples who lived that long ago. Here's a recent related post; follow the links to some lengthy threads, but in particular, the /r/AskScience AMA.