Similarly to your issue, I've been getting a message on my answering machine from a guy I've never heard of from a company I've never heard of, asking me to call him back. The number was long distance, so I just hit the delete key. Then he started asking for (not my name) to please call back. Again, I hit delete. If it had been a local number, I *might* have called it and said, 'You are calling the wrong number. (not my name) does not live here', but I don't feel obligated to do so.
I would delete and block the sender, if the email comes from a 'Do not reply' address. It is up to the participants in the arrangement to ensure they have the correct contact information for the other person. If there was an email address in the rental application, I *might* forward the email on to that person and let them know but again, I wouldn't feel obligated to do so.