A person who is not able to speak to a caller at the time a call is placed, telephones the person who called at a later time. The phrase used to describe this exchange of phone calls is “to return a phone call.”
This use of return is suitable in the context of telephoning, but it is not the best choice for other forms of communication.
In the context of written messages, “to return” is commonly understood to mean “to send back” or “to reject.” For example:
She returned his letters unread.
I keep getting all these emails returned undelivered.
Senders are getting their emails returned when sending to our gmail account.
Some speakers, perhaps by analogy with telephoning, use return as if it meant, reply, respond, or respond to. Here are some examples, together with revisions:
He returned my message right away.
BETTER: He replied to my message right away.
I suggested a date to visit his institution but he never returned my email.
BETTER: I suggested a date to visit his institution, but he never replied to my email.
The doctor never returned my message or sent any kind of confirmation that he received it.
BETTER: The doctor never responded to my message or sent any kind of confirmation that he received it.
They never returned my request for information.
BETTER: They never responded to my request for information.