Your Community picture is the photo people see next to your name in Community: the feed, crew lists, friends, messages and your public profile.
WHERE IT COMES FROM: the picture you add yourself (Community, your profile, Upload, Photos or Avatar). If you have not added one, and a tour manager put a photo on your tour crew card, Community shows that tour photo so people see your face instead of initials. Your own picture always wins: a tour photo never replaces one you added.
REPLACE IT: open your Community profile and tap Upload (or Photos or Avatar) under your picture, then save. Your own picture takes over everywhere.
TAKE IT DOWN: when a tour photo is showing, your profile says so under the picture. Tap take it down. Community shows your initials until you add your own, and the tour photo will not come back on its own, even if the crew card photo changes later.
TOUR MANAGERS: a photo you put on a crew member's card (Contacts) carries to their Community picture when they have an ATOM account and no picture of their own. Removing the card photo removes it there too, unless they added their own. People hidden on the tour roster are left out. The first time a tour photo becomes someone's picture, they get one bell notice that takes them to their profile.