Complete and reopen tasks
You can mark a task as complete by opening the Outlook task, and selecting Completed for the status, or clicking on the "Mark Complete" ribbon button in the task. The app will complete the task, and it will also complete all the task's children.
Tasks you complete today are shown struck-through, and are removed from your list after a day. However, they are not deleted, and you can reopen them. Reopening them puts them back on your list, and sets the status of the Outlook task to "In Progress."
To reopen a task that you completed today, and is still on your list, right-click on it, and select "Reopen Completed Task."
If the task is no longer on your list, you can search for it and reopen it by right-clicking on your task list, and selecting "Reopen completed tasks." This will show you a list of your completed tasks, which are shown struck-through (with their ancestors, so you can see the context). From here you can reopen a completed task by pressing the Reopen button. Reopening a task will also reopen any completed ancestors (but not completed children).
You can also permanently delete a completed task by pressing the Delete button.