Here is a sort of related article: Minoan Bronze Age mtDNA Study.

This article analyzes the mitochondrial DNA of modern populations and ancient human remains to discover who the Minoans (Bronze Age Crete) are descended from. The modern population of Crete are genetic descendants of the ancient Minoans analyzed in this study. Both populations (ancient and modern) appear to be genetically descendant from the same population that migrated from the Near East/ Anatolia (modern Turkey) to and throughout Europe.

The big deal about this study is that it shows that the Minoan civilization was not descended from Egypt or Egyptian civilization (the North Africa population).

My understanding is that near-total genetic cleansing is not terribly common (counter-example English/American conquests in North America and Australia), and probably almost never happens while preserving the indigenous language.

Even in places where the indigenous language is replaced or mostly replaced, total genetic replacement often doesn't happen, for example, the Spaniards conquest of Mexico/Peru.

Given the first point, I'd suspect that modern Greeks are related to Ancient Greeks to some degree. And I wouldn't be surprised if they even still have a significant pre-Greek genetic component.

If you do take this to /r/askscience, I'd be very curious to hear what they have to say about it and how they would even go about answering this question.

The problem with these kinds of questions is that they are rarely historically informed. I mean I once recall reading a study which tried to assess the Germanic component in the modern British by cfing modern British and...modern Germans and arguing based on those results. If something like that seems plausible to you, you lack logic.

With Greece ancient evidence is scarce, there have been some fascinating studies (such as the BSA study of the corpses in tomb B which proved they were related to each other, which is actually a big deal!) but...there's a lot of nationalism and jingoism.

Just look at Greece diachronically and you'll see how diverse it starts being from the Roman period onwards, you get huge areas which were given over to Slavic and Arvanite tribes by the Emperor in order to try to generate revenue. There are gigantic changes in things like topographic onomastics before the re-classicising period of the 19th century.

I think you'll find a substantial portion of the populace descended from pre-Greek peoples and a substantial amount of new-comers from the middle ages. Ironically most of the racists we have tend to look like Slavs lol. It's kind of interesting how stark the visual contrast in Greece is: you get islanders looking like they've stepped of Greek pottery and on one hand and people who could be Putin's cousin living in the mainland cities etc. I'm not saying visual appearance is a good key to genetics just that you need to think in terms of diversity and keep it historically informed.

You should try asking this in /r/askscience if you don't get any takers.