What is to be done to rid oneself of the sin of using a car that was bought with money from an interest-based bank, knowing that the buyer was unaware of that at the time?

It is forbidden to deal in usury, and whoever does so must repent and seek forgiveness. If your mother bought the car with entirely haram (definition) money, do not accept it, because haram money is not owned by its possessor, and it must be disposed of or returned. However, if your mother has both halal (definition) and haram money, there is no harm in accepting the gift, as it is possible she bought it with the halal money, unless it becomes clear that she bought it with the haram money.