This may be old news but we continue to have user’s computers incessantly prompting them to upgrade to Windows 10. Some may not mind this but most find this annoying enough that they are tempted to click on the link to upgrade just to make the icon go away. Most of the time an upgrade to Windows 10 works without issue but not everyone wants Windows 10 and certainly don’t want a persistent reminder on their desktop.
Good news is that you can easily get rid of the reminder without upgrading. You can uninstall a Windows Update KB3035583 and then hide it so that it doesn’t reinstall itself on the next update cycle.
Below is a link to a detailed article with step by step instructions and pictures on how to uninstall and hide the offending update.
Hope this helps!