Is that word supposed to be pyrrhic? Or Punic?

By the mid-4th Century at the latest Rome was well known at least to intellectuals in what would now be called mainland Greece. The sack of Rome by the Gauls at the beginning of the century attracted the attention of several Greek scholars, and it's possibly the earliest event in Roman history that we can be reasonably sure happened at more or less the same time as tradition tells us. Plutarch tells us that both Aristotle and Heraclides Ponticus, roughly contemporaries of each other in the 4th Century, mentioned the sack of Rome. Aristotle claimed that a man named Lucius saved the city (for which Plutarch chastises him slightly, reminding the reader that Camillus' name was Marcus), and Heraclides had a fantastic tale of the capture of the city by the Hyperboreans, whom he claims sacked a Greek city called Rome--that's interesting, that already Rome was being considered Greek, at least by some, and an idea that in later tradition would become quite common (Strabo, for example, claims that Alexander ordered the Romans to stop being pirates, and that Demetrius Poliorcetes made the same request, citing the common ancestry of Greeks and Romans). These are just passing references, though--Pliny claims that Theophrastus was the first to make serious reference to Rome, although the only surviving reference to the city we have from Theophrastus is a passing remark in the Historia Plantarum to the Romans sending 25 ships to Corsica. Hardly a detailed venture into the history of the city, although it's possible that in one of the dozens of titles that Diogenes Laertius attributes to Theophrastus a longer report was made--however, given their titles there's not much reason to suppose that Rome made up a significant portion of anything.

That's all literature, however. The cities of Magna Graecia had had contacts with Rome for centuries, going as far back as the Archaic Period, and even the cities of what we would now call the mainland had contact with the region. The connections with Magna Graecia are pretty firmly established--besides heavy Etruscan contacts, particularly with Cumae, we know that the Romans themselves had plenty of contact with the Campanian cities. But trade with the Greek mainland, particularly with Athens, is extremely old. Italy, and particularly Etruria, was one of the major centers of export for Greek, particularly Attic, pottery. In fact, we have so much Attic pottery from Etruria that it's been suggested (by Lissarrague for example) that much of what we consider to be characteristic of Attic styles may well have been specially-crafted for an Etruscan and Campanian export market (certainly things like vases depicting Aeneas carrying Anchises appear much more frequently in Etruria, where the cult of Aeneas is known to have been around in some force at a relatively early date). This raises the question of how distinct from Latium and Etruria was Rome at the end of the Archaic Period, and that's a question that's debated pretty heavily--while Etruscan influence is quite heavy in the city under fairly late, it's hard to tell just how much of a difference an observer might have been able to readily make. In any case, by a few decades before Pyrrhus' campaign the Romans surely would've been known throughout much of the Greek world, even if they were hardly a household name or of any particular importance (only one source makes mention of a Roman embassy to Alexander in Babylon, for example, and it's not a good one--Arrian, Plutarch, etc. make no reference to it, despite some of their lists of embassies being quite lengthy and detailed). But by the end of the Samnite Wars the Romans would've been in close contact with even the most southern cities in Magna Graecia, and were the hegemonic power in central Italy, enough so that Thurii felt that they were powerful enough to request aid from them