This was originally a question but I ended up finding a solution so I decided to post both in here in case others want to do the same thing.
I like to have control over when and if my system(s) perform Update tasks. As a result, I've configured Windows 10 Pro via Group Policy to the option to notify that updates are available, but wait for me to install them.
For the most part, this works exactly as it did with Windows 7 and 8.1. With Win10 I sometimes get a only mildly intrusive notification which doesn't prevent anything and just tells me there are updates. That's fine by me.
However, it would appear Microsoft is not in any way fine with this. At intervals, My entire screen darkens, and a single, small dialog appears stating that "Important Updates are Available". This dialog presents one option- "Get Updates". Pressing the button or escape has the same effect; it opens the "Windows Update" options in settings. I can only presume it tries to force the update to take place but cannot proceed because of the Group Policy settings.
This notification angers me unreasonably for some reason, though after mentally telling it off I've usually forgotten about it. What spurred me to look into it and try to do something about it was that I had the sheer audacity this evening to watch a movie. Right in the middle of the movie, suddenly I get the "Important updates are available" notification. It's crossed the line and now it must die permanently.
Also, just to cut off any alternate solutions "Just run Windows Update"- Aside from not wanting to wait a good 30 minutes to use my PC again, none of the updates it deems so are even important. There's a flash player update (Security updates are somewhat less important when the product in question is not even installed). There's a Windows Update which addresses a problem when a Windows 8 PC is upgraded to Windows 10, where Manufacturer bloatware is disappointingly removed, and an update to the servicing stack which applies to the creation of ISO media for Win10. "Important"? Hardly.
Anyway- on to the solution.
After some investigation I found that the notification itself is basically just Windows launching "MusNotification.exe" and "musnotificationUI.exe", presumably at times of it's own choosing for wholly undocumented reasons and triggers. Whenever it feels like it I guess, or Maybe once a day. Who knows. Anyway, This suggested to me that replacing those files with a do-nothing stub program might solve the problem. However, I'm sure the issue would be "fixed" in a later update- in that those files would return. So I decided to take a batch file approach. If I update later and Win10 reverts the behaviour, I'll be able to run the batch file to hopefully get it back to the way I want.
I created a do-nothing stub program by basically compiling the Visual Studio default template. The files in C:\Windows\System32 are set as owned by TrustedInstaller, so it was necessary to take ownership of the files, then give full control on the files to administrators. I then renamed the originals and copied the stub into their place. The batch file I ended up creating to do this looks like this. I was lazy and used absolute paths here so it's hardly a "generic" solution.
takeown /f C:\Windows\System32\Musnotification.exe
takeown /f C:\Windows\System32\MusnotificationUX.exe
icacls C:\Windows\System32\Musnotification.exe /grant Administrators:(F)
icacls C:\Windows\System32\MusnotificationUX.exe /grant Administrators:(F)
rename C:\Windows\System32\MusNotification.exe musold.exe
rename C:\Windows\System32\MusNotificationUX.exe musoldUX.exe
copy "C:\Users\BC_Programming\Documents\Visual Studio 2015\Stub\Stub\Debug\Stub.exe" C:\Windows\System32\MusNotification.exe
copy "C:\Users\BC_Programming\Documents\Visual Studio 2015\Stub\Stub\Debug\Stub.exe" C:\Windows\System32\MusNotificationUX.exe
pause
Now I wait and see if I ever see the notification again.