Could a short cause my bluetooth to not work properly?

I have a 2013 Honda CRV with about 2800 miles on it. I recently brought it in for an oil change and to have a recall taken care of. The recall was to stop the gear shift from moving when the brake was not depressed. When the mechanic inserted a pin which was the recall part, the pin shorted out. They went and got another pin from a 2013 car on the lot and that one shorted out as well after going from park to reverse. They put that pin back in the car on the lot and of course it didn’t work anymore. They then put me in a rental for the weekend and said they would have to call tech support Monday morning. On Monday they figured out what happened. When the mechanic took the gear shift apart, he moved another pin without knowing it so the connection was not complete causing the shorts. The dealer has accepted full responsibility for all of this. Well today I discovered that when I use my bluetooth in the car, the person i’m calling hears this really loud whirring noise, almost like when an alternator belt is screeching when they start to go. I on my end don’t hear anything but the person on the other end says it’s too loud to hear me. So I actually called and left myself a message at work and sure enough, I hear the loud noise. Could the short in the gear shift cause this? I wasn’t having any problems until this happened. Thanks for any help or advice you can give me.

I’m sure what they did screwed it up. There is service bulletins on updating the hands free system on the CRV. Maybe if they check the programming they could get it going again.