I am unaware of any connection between the Greeks and Palmyra.
The area was conquered by Alexander and became part of the Seleucid Empire, but they ignored Palmyra, which became independent until the Romans took it.
So, the locals would have been influenced by the Greeks as all in the region were, but there was no direct influence. Perhaps the author was using "Hellenistic" to denote the period after the fall of the Persian Empire and before the Roman conquest??