The opinions of the Greeks the Eastern world which notably included the Persians, Assyrians, Babylonians, Indians and Egyptians are known to all. They elaborated at length through their literature their thoughts on this matter and indeed it is certainly very interesting that we have so diverse a set of data from which we can pick out in detail their sentiments of the "barbarians" of Asia that were in the East from the Greek world.
However, prior and around the conquests of Alexander, I have yet to come across anything through which we may obtain any distinct notion of what these Eastern peoples thought of the Greeks. For example, the Persians were well acquainted with the Greeks yet we know nothing what they thought of them. Yet, the very identity of ancient Persia that we have largely comes from the writers of the ancient Greek world.
It should be kept in mind that when I refer to "ancient", I have in mind probably the period from 800 BC to about 100 BC. After this period, much data becomes available through the writings of the Jews and other peoples but I know nothing of the period before this.
It is significant that Berossus, a native Babylonian of the early 3rd century BC, appears to have written a history of Babylonia and certainly other things as well but I am not aware of any fragment of anything related to the Greeks in his work. Manetho is another good example, he seems to have shared his opinions of the Jews as we're well aware from the writings of Josephus centuries later yet nothing on anything related to Europe.
There is a silence, which is even terrifying to some degree, present in the Eastern literature regarding the world that laid in Europe. On the one hand, we have the Greeks who composed large compositions on the ancient world of the East, elaborated many of their manners and customs, their character, their government, their rites and whatever that seemed interesting and certainly the Greeks were very much interested in the world of Asia.
Herodotus' Histories may even be labeled a proto-ethnographical work, due to his great interest in the diverse customs of the world. The Greeks were highly fascinated by the peoples of Asia (which at that time largely included, if I am not mistaken, all the parts of the Achaemenid Empire such as Persia itself, Mesoptamia, India..etc). Another writer is Ctesias who is similar, and there is also Aristoxenus (a student of Aristotle) who tells us of an interesting anecdote in which Socrates is rebuked by an Indian philosopher, which seems that he may have had information available relating to the Brahmins. There is also Plato and Aristotle himself, in whose writings we find numerous references to the peoples of East.
Yet, what did the people of the East themselves think of the Greeks? Were they curious about them? Did they find anything unusual about them? What did they think about their customs? What did they think about their religion and their women? And more importantly, what did they think about their democracy which surely must have seemed something extremely strange? What did they find most "barbaric" about the Greeks?
All the data that we have on this matter I think comes from a time when the peoples of the East had been heavily Hellenized and thus I think there's significantly less of the "wonder" quotient. That's why I picked the period from 800 to 100 BC. Ofcourse, before 800 BC, we have not an negligible amount of references to the Greeks in the writings of the Hittites and Assyrians. Indeed, the famous "Philistines" it has been supposed may be the Greeks themselves by many scholars of this century, who so disturbed the Jews. Yet even there, we find not much of importance.
Thus the question may stated once again as simply as possible: The Greeks had a lot to say about the East, what did the East have to say? Did they said anything at all?