If you click on the three dot menu in the corner of the course card, then click on the Move tab in the popup menu, look to see if there is an option to Unfavorite. Try that first.
If you click on Courses on the far left, at the top is an option for All Courses. If you click/unclick on the stars to favorite/unfavorite, this can also be a way to adjust what is seen on your Dashboard.
Traditionally, when a course is complete, it will automatically drop off your Dashboard once the course term has ended, if the course has an end date. You can go to a course and click on Settings in the menu to see if it has a course end date.
Hopefully, one of these helps.