How can I clean these .MUM and .CAT files from failed updates?

Just for grins, I ran the following command at an administrative command prompt with voidtools (Search) Everything open and *.mum as the display criterion:

Code:

DISM /online /cleanup-image /startcomponentcleanup

The total number of objects before I started that operation was: 9,322. After the operation completed 20%, the total number was 6,940. It will take another 5 minutes or so for the command to finish, but I'll bet that the final count is even lower than it is right now. I'd say this provides proof positive that you can use this DISM command to clean up those files.
HTH,
--Ed--

You can use the DISM /remove-package command to target and remove specific updates in Windows 10, but you can use neither the KB number nor the Windows version number to target your removal efforts. It's more indirect than that, and requires some messing about with the list of installed packages to figure out what must stay, and what can go. I can't find a TenForums tutorial on this (anybody know of one? @Kari @Brink @essenbe @topgundcp @Bree) so I'll (reluctantly) point to this ArsTechnica piece: Removing Windows Updates via Command Line Not Working.
HTH,
--Ed--

DISM /online /cleanup-image /startcomponentcleanup is used only clean up the component WinSXS folder and is advisable after every cummulative updates, It will clean up quite a bit of space.
If you list all .mum & .cat files in deltail view, you'd see the date and also the KB in question. I have mine listed and most of them dated back in sept. 2017
These files are owned by Trusted Installer and cannot be deleted even if you are the Administrator.
Try:

1. Take ownership of these files and delete them. If failed, go to step 2
2. Download: PowerRun v1.3 (Run with highest privileges)
   then run. Click on the Command icon to run as Trusted Installer, cd to the folder then delete them.
3. An easy way is to boot up Linux then delete them.

If those KB's failed to update, you can safely delete them. Since I have a backup image, I booted into Linux and delete them all. Once back to Windows, Manually download the latest KB4093105 that update Windows to 16299.402 by passing all the updates in between.
You can use this link from @EdTittel post #1 or use mine in post #2 of this link, whatever you feel comfortable:
Download and Install Windows Update from Microsoft Update Catalog Windows 10 Tutorials

FYI, Even in this folder, there are thousands of .mum, .cat files but they don't occupy much space. After delete all the .mum and .cat files in mine, Windows re-created 1,668 files just to install KB4093105 and occupy 22MB total.

Great follow-up @topgundcp. Nice job of explaining what to do, and then pondering its advisability or necessity. You rock!
--Ed--