Within Teamwork Desk, you can delete an inbox via the inbox settings.
Click your profile icon in the top right corner of your Desk account and select Settings from the dropdown.
In the Settings area, select the Inboxes tab at the top, and choose the inbox you want to delete.
You can also access the inbox settings from the main Tickets area. In the left sidebar, hover over the name of the inbox you want to edit, and click the cog icon that appears to the right.
When viewing the inbox, scroll to the bottom of the Edit Inbox section and you will see an option to Delete Inbox.
Once you select the delete option, a confirmation modal will appear. If there are existing triggers or smart inbox dependencies, you will be alerted to these dependencies before confirming deletion.
Note: Deleting an inbox will remove the dependency between the inbox and triggers/smart inboxes.
For more information, see: Setting up an Inbox