Basically, it was something like this: Ashoka the Great sent missionaries in every direction. The most influential are the ones who permeated Southeast Asia. But the ones who traveled west ended up first in the Near East/Jewish world and later in the Greek world and there's maybe a translation that the term "Theravada" became Hellenized as "Therapudae."
And so the idea is that Buddhist monks introduced this asceticism tradition throughout the early Western world and that descendants of this tradition led to Jesus (among others) who preached similar values but from a Jewish framework/pantheon instead of the Vedic tradition.
Maybe a stretch, I haven't studied in an academic setting in a decade, but this reminded me of that idea. Thanks for sharing.