Once you have completed a task, you will need to mark it, to stop it from appearing in your tasks bar and also from the weekly task reminder emails.
You can perform this action in different ways as follows:
Navigate to the Tasks area ( click your profile, select Tasks, Show All) and click Completed.
In The Task List, under your profile view, set the complete bar to Yes.
In the Activity,where the Task was set, change the complete bar to Yes.
The task will be marked as completed and then be removed from your list and no further emails will be sent.