Microsoft has slipped adware prompting users to upgrade to Windows 10 into Windows Update, which for some was marked as important. That counts as shady business in my book, more so because as far as I understand it's not free but "free for one year", but even if I'm mistaken, this thing is annoying:

"Download Windows 10"
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 Windows update in which it came is very deceptive too:

"Update for Windows 7", "Install this update to solve problems in Windows", etc.; clearly not labelled as what it is, I guess I'm glad it didn't also include a browser toolbar nor change my home page.
The file that runs this is, in my case, "C:\Windows\system32\GWX\GWX.exe". Should I nuke the whole folder? The contents of it are:

Or should I just uninstall KB3035583? The description for it is so ambiguous I'm unsure if it's actually something that does more than just provide that icon.