Within Teamwork Desk, you can reopen Teamwork 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.
Select the checkmark to mark the task as complete.
To reopen the task, select the checkmark again.
For more information, see: Creating a Task in a Ticket