"How to Remove the “Get Windows 10” Icon from Your System Tray (and Stop Those Upgrade Notifications)." How-To-Geek. 5/23/16.
I ran the Never10 utility and it appears to have stopped those upgrade notices. I haven't been able to get it to delete the Windows 10 files secretly downloaded to my hard drive. The utility tells me that some of the files are in use and to restart and try again. The utility tells the same thing after I reboot so it looks like I'm stuck with about 1.7MB of those files.
The link above states:
Never10 was developed by well-respected security researcher Steve Gibson, which means it’s trustworthy and contains no adware, viruses, or other assorted malware nastiness up its sleeve. Basically, it acts as a frontend for Microsoft’s hidden settings that prevent the Windows 10 upgrade.FYI. Use at your own risk.
Also, commenter Carol at Liberty's Torch says merely removing Windows update KB3035583 solved the problem for her.
Commenter Rick C. flirts with heresy by saying just upgrade.