Within Teamwork Desk, triggers can be enabled and disabled as you choose.
To disable a trigger, click on the your profile icon to the top right of the navigation bar and select 'Settings:
Near the top of the page select the 'Inboxes' area of settings:
Select the inbox which has the trigger you wish to edit and select triggers from the left pane:
From this section triggers can be toggled on or off.:
For more information see: Editing or deleting a trigger