Change of visa with Global Entry
I am a UK citizen on a H-1B visa. I completed Global Entry enrollment today. The agent told me to make sure that when I enter I scan the visa page in my passport, not the regular ID page, otherwise I will be considered to admitted under ESTA. All that's fine and makes sense.
He then said: when you change or renew your visa, you're going to need to call us so we can register you under that new visa. He indicated that this is a formality, not necessarily involving another interview.
Has anyone had any experience doing this? How would I do it? Is there an option for it on GOES? Or do I literally phone them? If so, does anyone know the number? I'm probably going to renew my visa in about a year, so this is not urgent, but I'd like to know how it works while this is fresh in my mind.