Tangentially related, there is a Greek influence on Buddhism in East Asia because Buddhism arrived in China via the Greek Bactrian kingdom. The Buddha as depicted in East Asia is wearing Greek robes and there are elements of Greek philosophy in Buddhism as practiced in East Asia. https://en.wikipedia.org/wiki/Greco-Buddhism
Indeed, before the Greeks The Buddha would most commonly only be depicted by his absence, an empty chair or foot prints most famously. It's amazing that the iconography of a religion so ancient and "exotic" is so significantly shaped by European culture.
It's more an instance of convergence and mutual influence. Hellenistic philosophy (read: immediately after Socrates) went down a few different lines. The one with the largest influence in the West was the Academic line, concerned with empirical observations and theory making.
But another major line was about how to live well, and focused primarily on ethics and the virtues. Today, the most well known school in this line is Stoicism, and this approach to philosophy really has a lot of overlap with Buddhism. The Bactrians were extremely well primed to be receptive of some "wisdom from the East" (like the type Pythagoras was supposed to have received) that covered a lot of the same topics as Hellenistic philosophy.
By the time Buddhism was meaningfully re-introduced to European academics (starting around the 17th century, but culminating with Schopenhaur in the 19th), several writers once again remarked on the similarities between the Hellenistic and Buddhist traditions.