We just experienced a case where our helpdesk and the helpdesk of a partner company got into an autoreply war ( i.e. we forwarded a ticket to them, their helpdesk responded by creating a new ticket and sending a new ticket notification, we responded to it by creating a new ticket and sending a new ticket notification and so on ).
We believe that in the 'Edit Contact' page there should be an option saying "Do not send a New Ticket Created Requester Notification". This can be used, as a last resort, when you get involved in such a case.
Set up a Dispatch'r rule with the condition set
as 'Requester Email' 'Contains' [your partner's domain name], and action
set as 'Skip New Ticket Email Notifications' (screenshot below, for
Apart from the above suggestion by Freshdesk, one can also use another Dispatch'r rule with the conditions ( in Match ANY of the below ) set
as 'Description' 'Contains' [This is an automated message] + 'Description' 'Contains' [Your Ticket has been received and a member of our team will review it and reply accordingly.] + ..., and action
set as 'Delete the Ticket'
Note that Dispatch'r rule are evaluated in turn and first match wins ( meaning that once the conditions of a rule are fulfilled, the actions of that rule are executed and no further rules are evaluated ).