Most of the Greeks of Calabrians are now Italianized, but it is very likely that due to the mostly rural conditions of the region, the absence of significant foreign settlements and the late survival of Greek, that they may be largely descended from the medieval Greeks of the region, and even before that, the Greeks of mainland Greece. Moreover, since Greek settlement in Calabria largely pre-dates the descents of Slavs and Albanians in Greece, we may be able to (roughly) determine the extent of the impact of these elements in the modern Greek population.
Two papers in the literature [1, 2] report on the frequency of Y-chromosome haplogroups in the population of Calabira.  reports data labeled as "Calabrians", and  reports data on the population of Reggio and Paola. The cumulative sample has a size of N=87. Frequency data are shown below, with Greek frequency data also shown for comparison from 
Of course, frequencies may be modified by random genetic drift, and Calabrians are not descended from all Greek regions, but we can still make some general observations about their commonalities and differences.
In both Calabrians and Greeks, haplogroup J2 appears to be very frequent, and haplogroup E3b is also very frequent. It appears very likely that these two haplogroups were represented in ancient populations.
Calabrians have a higher frequency of haplogroup R1b. This haplogroup originated in Asia, but its most recent expansions mark the movements of people from Iberia and Anatolia after the Last Glacial Maximum. Italians have a generally higher frequency of this haplogroup, and hence it appears likely that R1b in Calabrians may partially represent the contribution of native Italians to their gene pool.
Calabrians also have a higher frequency of haplogroup J1. This haplogroup originated in the southern part of the Fertile Crescent, and is often (but not exclusively) found in modern Semitic speakers such as Jews and Arabs. This may represent remnants of Near Eastern people during post-Roman times, even though its earlier arrival cannot be entirely excluded.
Finally, a striking feature of the frequency table is the paucity of R1a and I lineages in Calabrians. R1a originated in the Ukraine and spread after the Last Glacial Maximum, but more recently with Slavic speakers. I1b originated in the Balkans and spread during late Paleolithic and early Neolithic and subsequent times.
It is fairly interesting that in a study which included a Cypriot sample , only 2% of Cypriots carried haplogroup R1a chromosomes. Cypriots are also a population which separated from mainland Greeks before the medieval period. The frequency of haplogroup I chromosomes is not available for Cypriots.
Also, of interest is the fact that in regions of Anatolia  inhabited by Greek speakers until recently, and in which the native population may be assumed to be descended partially from Islamized Greeks, the frequencies of haplogroups R1a and I are also low. In the Aegean region (8) they are 3.3% and 6.7%, and in the eastern Black Sea region (3) where Muslim Greek speakers still exist, they are 4.8% and 2.4%. Moreover in Anatolia R1a1 frequency is correlated with longitude, declining towards Greece. R1a frequency also decreases from north to south in the Balkans .
In conclusion, this small survey provides some evidence against the notion that Y-haplogroups I and especially R1a were substantially represented in ancient Greeks. The relative absence of these haplogroups in populations thought to be partially descended from Greeks, in addition to the decrease in frequency of R1a both north-to-south in the Balkans and east-to-west in Anatolia are the main reasons for this observation.
Naturally, I doubt that we can statistically exclude the presence of either haplogroup -at some low frequency- in ancient Greeks using these relatively small samples, but at least we have some indication that they probably did not form a substantial part of their patrilineal descent.
In a larger sample of Calabrians, the haplogroup I frequency is 5.4%, and that in Sicilians is 8.8% . Haplogroup I lineages in the Balkans and Italy are divided mainly into I1a, I1b, and I*(xI1a, I1b).
I also came across this interesting paper (Coll Antropol. 2001 Jun;25(1):189-93.) which further substantiates the idea of the genetic isolation of Reggio Calabria, listed as REG above:
Surnames of grandparents were collected from children in the primary schools of the Albanian-Italian, Croat-Italian, and Greek-Italian villages. The coefficients of relationships by isonymy show almost no relationship with ethnicity. Ethnolinguistic minorities of Southern Italy and Sicily are geographically subdivided in two main clusters: the first cluster comprises the Albanian, Croat, and Greek communities of the Adriatic area; and the second cluster comprises the Albanian communities of the Ionian, Thirrenian and Sicilian area. The Greeks of Reggio Calabria Province are completely separated from the other communities.It would be extremely interesting to see a study that focused only on Greek speakers of Reggio Calabria.
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