Receiving email from generic email accounts

We have a few services on various servers that will send emails to our helpdesk. For example our backup server will send an email to the helpdesk email address when a backup fails. The problem is that the sending email is a generic email address that doesn't really exist. So naturally ServiceDesk will receive a failed bounce back message when it responds to a new request. The result is that ServiceDesk will add notes to a ticket stating that there was a failed bounce back message. Is there anyway to configure ServiceDesk to NOT makes notes about any bounce back messages or is there a way to stop sending response to certain email address?

Thanks in advance for any help.