Within Teamwork Projects, if you are an administrator, you can change the Date Completed information on a task.

Click the completed task name to go to the Task Details screen. In the left panel, you will see a Modify link next to the Date Completed.

You can choose a new completed date here, as well as the person who created the task, and the person who completed it.

Click Apply Changes to update the task information

For more information, see: Changing the creator of a task