Within Teamwork Desk, you can reopen Teamwork.com tasks that are attached to existing tickets.
When you are viewing a ticket, go to the Tasks tab. You will see a checkmark to the left of any tasks attached to the ticket like you would in Teamwork.com.
Select the checkmark to mark the task as complete.
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To reopen the task, select the checkmark again.
For more information, see: Creating a Task in a Ticket