Users really like to see their green thumbs up on the dashboard, but what if they have a course that's stuck?
The task list is driven by completion of courses, meaning a mandatory course will not fall off the my task list until it is in a status that equates to complete. A no show status does not fulfill the requirements for completion which is why it remains on the task list. Typically, after a no show, the user would move to another instance, complete the requirements, and it would then come off the list.
If a course is no longer a required, you can mark it cancelled and indicate one of the reason options such as 'no longer required' and it should still show in the user's profile on the Enrollments tab, and the no show should be visible in the Session Details.