There was, as far as we know, no influence between classical Greek philosophy and Indian philosophy. (Classical Greek philosophy is 5th- and 4th-century BC philosophy, until the death of Aristotle in 322 BC; this category, therefore, includes Heraclitus, Parmenides, Plato, Socrates, etc.)

There was no Sanskrit-Greek translation movement. This gets at the heart of the reason why there was no interaction between Indian and classical Greek philosophy: there just wasn't the opportunity for it. I'll also add that, at least as far as classical Greek philosophy is concerned, there just wasn't much of a desire for it. Especially for Athenian philosophers, such as Plato, it seems that philosophy was tied inseparably to life in one's own political community. The one moment in all of Plato's dialogues where the main character, Socrates, leaves the city and is seen in "nature" is striking. This sensibility really doesn't lend itself to looking to ancient India for... what, exactly? More interlocutors?

Only rarely does Plato look outside Greece. Occasionally some of the myths he invents are attributed to Egyptians, but the significance of this is unclear. It doesn't seem to carry any importance beyond, merely, a hand-wavy way of indicating: 'this myth should command your respect because it is so old that we don't really know its origins!'

Also, philosophy in Athens at the end of the 5th century BC and for much of the early 4th century BC (so, when Socrates is active and when Plato begins to write dialogues) is an opportunity for reflection on Athenian life after Peloponnesian War, which the Athenians decisively lost and then had been punished for (but not excessively) by the Spartans. Athenian democracy was in a crisis, and itinerant teachers, called sophists, were causing a fuss. For this reason, some scholars have even thought of philosophy as a 4th-century BC invention. (See Gisela Striker, "The Methods of Sophistry.") My point is that classical Greek philosophy lacked the opportunity and desire to look to India. We might view philosophy as a "Great Conversation" today -- but classical Athenian philosophers viewed their interests differently.

But notice that I have been talking about classical Greek philosophy. The period of philosophy that starts after Aristotle's death in 322 is called Hellenistic philosophy, and there, we get a story of an interaction

Diogenes Laertius tells a story of Pyrrho of Elis, while writing his biography. He says that Pyrrho went to India and met some 'gymnosophists'. These are the words Diogenes uses: 'gymnosophists and Magi in India'. What is a gymnosophist? Well, the word 'sophist' literally means 'a wise person' (but almost in a professional sense: it isn't the adjective for 'wise' being used, but a related word that denotes something like it is one's job to be wise -- related to the idea that the core of being a sophist was being a teacher who got paid for teaching people). 'Gymno' comes from the Greek 'gymnos' meaning 'naked'. These were, literally, naked wise men.

To give some idea of the dates we're talking about here: Diogenes Laertius lives from 180 AD to 240 AD; Pyrrho of Elis lived much earlier, flourishing at the start of the Hellenistic period, living from 360 BC to 270 BC. Diogenes Laertius is, therefore, reporting this story long after Pyrrho of Elis lived, but he does seem to be drawing upon independent sources that corroborate his account. Besides, many of his biographies uses sources that are actually contemporaneous with his subjects' own lives, which speaks in favor of his credibility -- at least sometimes. The fact that, during this very period, the independent Greek political communities (i.e., the polis) were losing their independence marked serious revisions in the attitudes that I said held up in classical Greek philosophy.

OK, so what does Diogenes Laertius actually say happened in this meeting? Well, he tells us -- twice, in fact (IX 63 and IX 69) -- that it was while meeting with these thinkers that Pyrrho of Elis decided to become a skeptic. This is quite a significant moment in the history of Hellenistic philosophy, then, because he is the founder of Pyrrhonism, an important skeptical school of philosophy. If true, this story means that, in at least one important way, the development of Greek philosophy was influenced by Indian philosophy.

Who were the gymnosophists? Well, scholars (see especially Flintoff below) aren't sure. There were groups of Buddhist and Jain ascetics who would fit the bill, but it isn't really clear. The Buddhists in particular had skeptical strains of thought that make them good candidates.

Who were the Magi? It is sometimes floated as a possibility that these were Iranian priestly Magi, but the use of this particular Greek word here ('magos') in this very context heavily suggests that there were some holy men from India itself.

So, you'd think this would be decisive. But in fact, many historians of Greek philosophy prefer to discount this origin story of Hellenistic skepticism. Trust me, they all know the story, but it is hard to see what sort of explanatory power the story has. A.A. Long in his book Hellenistic Philosophy (London: 1974; pg. 80) says "It is impossible to know whether oriental influences played any significant part in Pyrrho's philosophical development. The evidence does not require such a hypothesis." In other words, we know so little about the gymnosophists -- who they were, what they actually said to Pyrrho -- that the theory that Pyrrho got his views from them doesn't really explain anything. For instance, we don't know whether this means he got the mere idea of skepticism from them; whether he refined their ideas; or whether he endorsed everything, whole-sale. There just isn't enough detail in Diogenes Laertius' story to say much more than what I've said: Pyrrho of Elis is said to have become a skeptic after meeting the gymnosophists and magi in India.

Flintoff's study, listed below, is the best example, in my opinion, of a scholar pushing back against Long's position and arguing that we really, really ought to use this story to explain features of Hellenistic skepticism.

Recommendations:

This short video from Prof Peter Adamson: https://www.youtube.com/watch?v=Yc6RfRTIgFo

This podcast from Prof Peter Adamson: https://historyofphilosophy.net/india-greece

Sources:

C.I. Beckwith, Greek Buddha: Pyrrho’s Encounter with Early Buddhism in Central Asia (Princeton: 2015)

G.P. Conger, “Did India Influence Early Greek Philosophy?” Philosophy East and West 2 (1952), 102-28.

E. Flintoff, “Pyrrho and India,” Phronesis 25 (1980), 88-108.