Once you have completed a task, you will need to mark it as completed to stop it from appearing within your tasks bar and also from appearing within the weekly task reminder emails.

To do this, navigate to the Tasks area (by clicking your profile > Tasks > Show All) and click Completed:

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You can also complete the task within the Task list in the profile view:

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Lastly, you can do this where the Task was set in the Activity:

The task will be marked as completed and then be removed from your list and no further emails will be sent.