Microsoft has slipped adware prompting users to upgrade to Windows 10 into Windows Update, which for some was marked as important. It's an icon in the taskbar, which has a menu of four options related to the offer and no option for removing it. The file that runs this is, in my case, "C:\Windows\system32\GWX\GWX.exe".

I managed to solve it (getting rid of the system tray icon) by renaming the folder from: C:\Windows\system32\GWX to: C:\Windows\system32\MicrosoftKeepYourMalwareHome.
and rebooting. Which seems to work fine, Process Hacker doesn't show anything weird running.