This new study is mainly about Peloponnesean Greeks and how they haven't changed much since ancient times, but they also happen to be the group of Greeks who are genetically closest to Southern Italians. In addition to 5 Italian samples from all over the country, the study also has a large sample of Spaniards (including Andalusians from the south), who are genetically closest to Northern Italians.
Confirming many other studies, this PCA plot shows that the Italian samples — Lombards (labeled "Italians"), Venetians, Tuscans (including "TSI"), and Sicilians — cluster in a North-to-South cline between the Spanish and Greek samples, i.e. Southwestern and Southeastern Europe on the map. (Sardinians, as always, are outliers because of their almost purely Neolithic farmer ancestry.)
In these plots, with the Peloponnesean Greeks (in red) acting as a proxy for the southernmost Italians (and therefore all Italians and Southern Europeans in general), we can see that they're genetically distinct from all non-European populations of Western Eurasia, North Africa and beyond.
Stamatoyannopoulos et al. "Genetics of the peloponnesean populations and the theory of extinction of the medieval peloponnesean Greeks". Eur J Hum Genet, 2017.