Alert about bounced emails using Spring Boot

I have a Spring Boot application that sends emails. For any action that requires notification, a Mail instance is created with status PENDING in the database and a job is run to send the pending emails every minute. The status of the Mail instances are set as PENDING, SENT or FAILED.

try {
    Properties props = new Properties();
    props.put("mail.smtp.auth", "true");
    props.put("mail.smtp.starttls.enable", "true");
    props.put("mail.smtp.host", host);
    props.put("mail.smtp.port", port);
    props.put("mail.smtp.from", myEmailAddress);
    props.put("mail.smtp.timeout", 2000);

    Session session = Session.getInstance(props, new javax.mail.Authenticator() {
        protected PasswordAuthentication getPasswordAuthentication() {
            return new PasswordAuthentication(username, password);
        }
    });

    MimeMessage message = new MimeMessage(session);
    MimeMultipart content = getContent(mail, message, username);
    message.setContent(content);
    Transport.send(message);
    mail.setStatus(MailStatus.SENT);
    mailService.save(mail);
} catch (MailConnectException mce) {
    mail.setStatus(MailStatus.FAILED);
    mailService.save(mail);
} catch (Exception e) {
    // other actions
}

Now, this works fine if a valid email id is provided. But when the receiving email address is a non-existent one like somerandomname@gmail.com, there are no exceptions thrown. From what I read from similar questions in SO and elsewhere, I understand that mail sending is an asynchronous process and hence there is no way to determine that a given email is existing or not (or other issues like Inbox full). That is why after the Transport.send(message); statement, the mail.setStatus(MailStatus.SENT); statement will always be executed irrespective of the email address being present. Later the mail will actually be attempted to be sent and I get an email in myEmailAddress with content like the following:

The response from the remote server was: 550 5.1.1 somerandomname@gmail.com User unknown

Okay, accepted until this point. But now I need a way to alert the user that the email couldn't be sent because they entered an invalid email so that they can update their email. More specifically, I need to set the status of the Mail instance to FAILED. What is the best way to achieve this?