Careless driving
MCL 257.320a(1)(m) assesses 3 points for careless driving under section 626b. MCL 257.320d(3)(d) then rules out a violation of section 626b by name, so the Basic Driver Improvement Course cannot be used for it even though it carries only 3 points.
What the points do
A Michigan court that convicts a driver of a moving violation sends an abstract of the conviction to the Secretary of State, and the point value from the schedule in MCL 257.320a attaches to that abstract. Points stay on a record for two years from the date of the conviction. A non-moving violation produces an abstract with no points on it, which is the whole of the difference behind a plea to one. How points reach the record goes through this in full.
The basic driver improvement course
MCL 257.320d does not cover this kind of violation, whatever a particular driver's record looks like. The exclusions in subsection (3) work by the kind of offence, and a violation that adds no points to a record has nothing for the course to withhold.
This is general information from a driver-safety school. It is not legal advice. Your court can tell you what it requires, and an attorney you hire can answer questions about your own case.