I have heard multiple perspectives of the story of Hanukkah, but a main belief seems to be that it was a civil war between to sides of jews, not a war between the greeks and the jews.
However, I have not found any information on how the greeks reacted to the civil war, assuming that is what took place.
The fact that you can't find any sources tells you exactly what you need to know. You're not likely to find much of this history outside the accounts of 1st Maccabees and Josephus' Antiquities, books XII-XIII.
We need to remember that to the Hellenistic kingdoms and the Roman Empire Judaea was often just a poor backwater that was only of interest because a) it was strategically located between Egypt and the rest of the ancient Near East and b) the Jewish people were a curiosity with their quirky religious practices and tendency to revolt.
While we can't and shouldn't underestimate the contributions of ancient Judaism to Western Civilization, we also have to remember that their outsized influence doesn't equate to great political significance at the time.
The Seleukid monarchs sent generals with armies to fight the Maccabeans and there were battles but small skirmishing between the Jews was normal. Judas Maccabeus himself was defeated in battle and killed by the general Bacchides but due to the chaotic political situation and advancing Parthians the Seleukid kingdom later gave the Maccabeans independence. My sources are primarily from Bar Kochvas "The Seleukid Army".