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Ok there are 3 ways you can have a Facebook thing on your iPhone homescreen. You can have 1 of two apps, the Facebook app itself, OR Facebook messenger app, you'll know the difference RIGHT away as the Facebook app has the big F, and Facebook messenger has a chat bubble. And the 3rd thing would be a home screen link to the Facebook web page. This is rare and you probably wouldn't even know how to do it let alone have one on your home screen.
NOW what might have happened here, is you may have moved your Facebook or Facebook messenger icon in to a folder (or created a folder) by mistake. To find out do a "spotlight search" on your device. Swipe down, then type Facebook (both Facebook AND Facebook messenger should come up), and when the results come up IF any are in a sub folder it will be listed to the right of the result, just find that folder on your home screen and then move it out!