When a student drops (or is removed from) a Blackboard course, their course availability gets set to "No"

and the account gets marked with a (\) in the Grade Center:

Students so marked do not see this course on their My Courses list. They cannot access the course and they cannot view the course's content, and they're not factored in the Grade Center's average (if you're exposing that to students).

If you'd like to have the student dropped from your Grade Center list as well, you can use the HIDE ROW tool to remove it from your view.

Just go to the course Grade Center, point to MANAGE, then choose ROW VISIBILITY.

Check the box to the left of the row you want to hide, then select HIDE ROW at the top or bottom of the list. Click SUBMIT to save your change.