It is well known fact that an old update flagged as Important in Windows Update is known to create problems for some users, while it is not known to create any problems if it is not installed.
KB971033 was released as Update for Windows Activation technologies.
https://support.microsoft.com/en-us/help/971033/description-of-the-update-for-windows-activation-technologies
In fact, this update is supposed to verify with Microsoft back-end servers if the key used in the process of activation Windows is legit or not. It is not known if those servers are actively maintained or if they function as intended. There are many cases of documented problems with repeated activation with legit keys or other instances when the key is legit, while the result provided by the activation servers says differently.
The main problem is that when a Windows installation has been flagged as non-legit, the procedure to recover require advanced knowledge and is not widely known. It is not a matter of uninstalling KB971033 any longer. However, installing and uninstalling KB971033 using the normal procedure is clean if the installation was not flagged as in breach of licencing agreement.
There is a less known issue with this update (and any other Important update) being left not installed in the list, but at the same time not hidden. This does not apply to Optional updates and Recommended updates not installed when they are seen as Optional, only to those updates in the Important list which in theory should all be installed.
When KB971033 is left in the list and neither installed, nor hidden, it will block the installation of critical updates which are always installed only when there are no other updates available, as they have to be installed by themselves. One well known example is KB3177467
https://support.microsoft.com/en-us/help/3177467/servicing-stack-update-for-windows-7-sp1-and-windows-server-2008-r2-sp
If this update is not installed, other critical updates which require it will not be installed and will not even be visible or possible to install manually.
In summary, the only correct procedures to patch in relation to KB971033 are:
1. Install KB971033 and forget about any of those written here, but taking the risk that at some stage, due to an unpredictable glitch, the Windows 7 installation is made unusable by Microsoft activation servers. I see this option as risky and not recommended. However, if nothing unexpected happens, Windows Update would work as expected and correctly.
2. Do not install or uninstall KB971033 if installed and hide it. Hiding in this context is essential for correct functionality of Windows Update moving forward.
3. Do not install or uninstall KB971033 and do not hide it. Download and install manually KB3177467. This is a perfectly functional option, but require a little bit more attention with Windows Update.
Note 1: Those familiar with my posts on this site are well aware that I am against hiding patches. This is one notable exception because KB971033 is not dynamic in nature, in not superseded or superseding other patches and has not changed since 2014 when it was released. It is not likely that this will change in the future, because this concept of activation verification is largely obsolete now.
Note 2: Those running Enterprise versions of Windows 7 and managing them via WSUS, may have noticed that KB971033 is not available in WSUS. This update is not available in Microsoft Catalog either. There are known issues with KMS Activation and KB971033 which require this update not to be installed, due to conflicting licensing mechanisms, in this case retail vs volume licensing.
https://support.microsoft.com/en-us/help/4032981/powershell-script-for-windows-7-non-genuine-issue-is-available