Upon starting the car, the ignition continues to make a harsh noise... on 2008 Hyundai Sonata

... Like when you turn the ignition on when the motor is already running. I also hear this noise sometimes when shifting into or out of parking gear (auto). What could be the cause?

Sounds like a transmission issue. Do you have any check engine lights on?
Thanks. I kinda suspected that too... But my mechanic thinks I need a new starter.
Your starter would not make noise shifting from any gear to any other gear.
Yup, I said that too! But he says there is a flywheel, a part of the misbehaving starter unit, that is probably continuing to brush against the transmission instead of retracting once the engine is started,causing that sound. This should naturally stop when the starter is replaced, he said. (Or something like that!) I think I'm going to try that... Again, thanks a lot for your input.