If you rewrite the sentence this way - She wanted to know if he had a car. then no, it's not necessary. Otherwise, I think your sentence should be written like this - She wanted to know whether or not he had a car.
New words, one handy idiom, and a 2-minute quiz — delivered to your inbox to keep your streak alive.
vsureshIs or not necessary here?No. "or not" commonly occurs with a whether-clause, but it's never required.