Disable Client side notifications for specific user/email address

One of the emails we receive tickets from in our help desk is another help desk.  We are looking for a way to disable the client side notifications of "New Open Ticket" or "Ticket has been closed" etc.. just for them, while keeping it alive for everything else.  I tried creating a separate tech group, with a separate email address and unchecking the Request Type from the "Open" email template, but they still seem to send.  I'm not sure if there is a round about way of doing this, but I am open to any suggestions on this one!  Pretty new to the Web Help Desk system right now.