Sage Advice has weighed in on a similarly worded game feature (p. 6):
Does the warlock’s Awakened Mind feature allow two way telepathic communication? The feature is intended to
provide one-way communication. The warlock can use the
feature to speak telepathically to a creature, but the feature
doesn’t give that creature the ability to telepathically reply.
The text of Awakened Mind states (PHB, p. 110, bold added)
You can communicate telepathically with any creature you can see within 30 feet of you.
This is linguistically very similar to the text in Find Familiar's description, which states (PHB, p. 240, bold added):
While your familiar is within 100 feet of you, you
can communicate with it telepathically.
Given the clarification of the meaning of Awakened Mind in Sage Advice, and the alteration done to Find Steed but not Find Familiar, there's a lot of evidence that Find Familiar's telepathic communication is meant to be one way.
But it's unclear
Despite the evidence given above, it'd be unrealistic to say this issue is definitively decided. After all, the most common way that something becomes a Sage Advice question in the first place is that the rules are sufficiently unclear that many people are confused: and Find Familiar has the same unclear wording as Awakened Mind. As written, the text gives enough ambiguity that there's leeway for any particular group to rule on this as they see fit. To add to this, Jeremy Crawford's own opinion on the matter is the opposite of my previous conclusion (credit to V2Blast for finding this):
I allow a familiar to telepathically communicate simple concepts to its master.
Since he says "I allow," it seems this statement is meant to indicate a decision as a DM, not as a designer of the rules. So it leaves the decision in the hands of the DM.
Besides, the ability to look through a familiar's eyes and hear through its ears would make most things it could want to communicate to you superfluous. And it certainly stops the familiar communicating you from being unbalancing in most cases.
You could even take the change to Find Steed's text as a piece of evidence in favor of the idea that familiars can communicate back. After all, the change implies that the phrase "communicate with" was meant to allow two-way communication in the Find Steed spell, so it might be meant to do the same thing in the case of Find Familiar. The lack of similar change in Find Familiar in the last errata makes this conclusion suspicious, but we cannot read anything definitive into a lack of a change: we can't interpret rules that don't exist, only the ones that do.
So although most evidence points to the conclusion that you can send telepathic messages to your familiar, but they cannot telepathically respond, it's sufficiently unclear that it's left up DMs.