This has come up before with the suggestion being to just null route the mailbox on the server side to prevent the bouncebacks (or configure your SMTP server to just silently drop the replies).
I like the idea, don't get me wrong. My issue is I struggle to justify adding and maintaining a feature that will, effectively, be used at most once per instance for most people. Maybe twice if you're weird and you're running two monitoring systems or something.
I would much prefer to hard-code something into the ticket parser that skips the email notification if the email contains the phrase "noreply" or "no-reply".
But maybe in wrong/lazy for suggesting this.