Restarting didn't work. So I backed up to the Cloud via that horrible message's interface, and I was honestly terrified. So easy it would be to lose my precious Contact, Notes, and Calendar data!
Over 600 people have clicked on "I have the same problem" in forums dealing with this bothersome persisting message in Settings. I would suggest a "Cancel" or "Use another form of backup" button for people like me, who have no need to back up their phone to the Cloud.
In order to rid the phone of that message, the user must back up their whole phone to iCloud, but to do so, the user is required to set up 2-factor authorization. So I set it up. But then I learned that I could never turn 2-factor authorization off!
I did more research and finally learned that I could turn off 2-factor authorization, but the illogically written instructions in my confirmation email (confirming that I'd turned 2-factor authorization on) gave me no choice but to basically agree that somebody had used an unfamiliar number to back up my phone! That was the only choice I had when clicking the link in the email to undo 2-factor authorization. And I was forced to change my Apple ID password! In addition, if I had waited more than 2 weeks to undo 2-factor authorization, I would have NEVER been allowed to turn it off.
I finished my Cloud backup, and went through the workaround provided by a very clear YouTube video to turn iCloud backup off and delete the backup.
What a relief. The bothersome message disappeared from Settings and my phone was in good working order with no data lost.
It will be awesome when Apple starts logic-checking choices in dialog boxes more thoroughly. The experts in the Apple Store can navigate these choices because they have memorized them, but many of them make no sense, in terms of the logic of language, even to high-tech people such as myself, if it the first time we're reading them. I hope the problem of this persistent unwanted message in Settings, which has been troubling users for a while now, will disappear in the next iPhone update.
[Edited by Moderator]