The Google Script scans your Gmail mailbox for messages from mailer-daemon@gmail.com and prepares a bounce email report logging the failed deliveries in a Google Spreadsheet. See sample Gmail bounce report

function getBouncedEmails() {
  /* Written by Amit Agarwal */
  /* Email: amit@labnol.org  */

  // Write the bounced email report to a Google SpreadsheetApp
  var sheet = SpreadsheetApp.getActiveSheet();
  sheet.getRange(2, 1, sheet.getLastRow(), sheet.getLastColumn()).clearContent();

  // Find all emails returned via Gmail Mailer Maemon
  var query = 'from:(mailer-daemon@google.com OR mailer-daemon@googlemail.com)';

  // Get the most recent 500 bounced email messages in Gmail
  GmailApp.search(query, 0, 500).forEach(function (thread) {
    thread.getMessages().forEach(function (message) {
      if (message.getFrom().indexOf('mailer-daemon') !== -1) {
        var body = message.getPlainBody();
        // Get the bounced email address from the body
        var matches = body.match(/Delivery to[\s\S]+?(\S+\@\S+)\s([\s\S]+?)----- Original Message/);
        if (matches) {
          // Get the exact reason for the email bounce
          var reason = matches[2].match(/The error.+:\s+(.+)/) || matches[2].match(/Technical details.+:\s+(.+)/);
          if (reason) {
            // Save the data in a Google Spreadsheet
            sheet.appendRow([
              thread.getLastMessageDate(),
              matches[1],
              reason[1].replace(/ (Please|Learn|See).*$/, ''),
              thread.getPermalink(),
              thread.getFirstMessageSubject(),
            ]);
          }
        }
      }
    });
  });
}