I had that done many years ago. They removed the whole gland. Have a pretty scar on the side of my neck. I ended up having some kind of damage from the surgery where the muscles in the side of my neck feel like they "catch" on I have to stretch my neck funny for it to feel better. It's probably some scar issue or something.
Now mind you I had this done probably 20 years ago so I'm sure they do a much less invasive surgery now.