Thank you for confirming I am not the only one! I managed to reproduce this in a verizon store and a salesperson and manager heard it. They both said they never heard that sound before on any other phone on their network and were confused. They called an LG rep who is going to come look at my returned phone next week. I am on my third LG G2 with this problem and it's still happening. I am in contact with tech support and tomorrow the Verizon network team is going to analyze some calls I made with the problem, somehow. I'm not sure what they're going to discover, if anything.
I may end up switching to the Moto X and hoping that's better. I wasn't sure if I have some weird issue with being on 4G network where I use the phone but it doesn't make sense to me that my 3G fascinate works fine for voice in same areas.
By the way, my second G2 phone which I only had for a few hours, started overheating (see LG gets hot threads). Oh, and this third phone also has the other odd issue of doing high pitch buzz in-between my spoken words which is only heard by some phones or answering machines. The display unit in the verizon store does this too.