Reboot fixed it. I’m hoping it was not some nefarious thing running in the background. It has not come back.
Hey! Found out what this white "dot" is! This particular one can also be two white dots! If you're ever doing a copy/paste on an iPhone or an iPad, the selection is marked by a blue line and dot at either end (see attached). If this selection is somehow transferred or located in the search bar at the top of the iPhone/iPad screen after a halfway down swipe down on the Home Screen (with me?), then the two blue dots can remain in this search bar, however, they turn white when they're here, and one or both may remain on the Home Screens(s)...this glitch is reproducible (after I had the white dot thing) and is cured every time by the "Reset Home Screen Layout" command!