Yes, those 2 points can be removed by taking a NJ Motor Vehicle Commission ("MVC") approved driving class. (A list of approved classes is on the MVC website.) BUT, please note 2 things:
1. Your insurance premium may not be affected if you only have 2 points. You should find out before you go through the hassle of enrolling (and paying for) a driving class.
2. What MVC doesn't tell you is that after completion of a driving class, you are placed on the equivalent of "probationary" status for at least 1 year, during which if you have any new motor vehicle infractions, there can be serious consequences, including in some cases, a license suspension.
Moral of the story: It may be better just to keep the 2 points.
You can remove the points with an approved safe driving class. How that effects you insurance must be answered by them. Some will honor the reduction others charge by the "event". Call the company.
If you have a copy of your policy, you should review it. Different insurance companies have different rules governing the assessment of points and the effect on premiums. If you don't have the policy, just make a phone call and ask the company directly....it's not like they wouldn't eventually learn of the situation anyway.
Insurance points are separate to NJMVC points as at least one attorney already accurately reported. Even if you manage to eliminate your NJMVC points with a class, the class may only be of minimal benefit with respect to your insurance premiums. And it may be of no benefit at all if you get another 2-pointer ticket within the next three years. It's compicated. Check with a lawyer for a full explanation.
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If you don't receive another ticket within a year, the two points will automatically be removed from your driving record.