Request (created via email) do not bounce for people not on the customer list

If a customer on the customer list (request security customer list) sends an email, that gets converted to a request, however if someone not on the list sends an email the email just goes to the mailbox, the user is not notified that he is not allowed to send emails to the service desk and the service desk agent does not get notified either.

We can create mailbox restrictions who can send emails to that mailbox, but that would mean double work, once on the Jira side and once to allow same customers to send to this mailbox on the mail server.

Am I missing something ?