How does a person handle the gag reflex during the procedure. Can this be done under anesthetic?

You will be given relaxing medication to put you into a twilight sleep so that you are in a relaxed state and don't remember the procedure. 

Hi, 
The Orbera insertion and removal procedures must be performed under anesthesia. This is usually a "twilight" type sleep, not general anesthesia, meaning you are breathing on your own but in a deep, comfortable sleep. I would not worry about gagging. In fact, you are very unlikely to remember even having the procedure. The most commonly used anesthetic is Propofol. This is a very safe, fast acting medication, which also exits your body very rapidly after the procedure. You will only be groggy for a short time afterward.