The Hittite Civilization lasted until the arrival of the Sea Peoples, in a period known as the "Late Bronze Age collapse". The other civilizations that collapsed in this period were also the Ancient Greek civilizations of Mycenae and Crete. After the collapse of the Bronze Age civilizations of Greece, there was a 400 "dark age".

Herodotus, an Ionian (a Greek who lived in Asia Minor (that is to say, living near the former Hittite lands) does not discuss at all the Hittites. Nor did Pausanias, who was also from Ionia.

To answer your question, the Ancient and Classical Greeks knew nothing at all. For that matter, deither did the Romans.

ed:clarification