On an iPhone you can go to Settings -> Name, Phone Numbers, Email -> Edit Reachable At. That's one way I guess. Haven't used this menu before so not 100% positive.
True - maybe it shows it afterwards, but adding a new phone number doesn't require password entry or Face ID. As for removing the existing number, I can't remove mine until I de-register it from iMessage & Facetime (since it's the number on the phone), so maybe they turned those off or they popped in a new SIM card.