I've come up with a little trick as follows to command MB's artist thumb retrieval behavior.
If MB cannot find a thumb for an artist to retrieve, it creates a zero-byte PNG file in the thumb cache folder and stop attempting to search for that artist afterwards. Then all you need to do is to add a zero-byte PNG file in the cache folder for artists it had downloaded an album cover or any other unwanted picture in order to keep MB from attempting to re-download them after you removed those pictures.
So when auto-downloading of artist thumb is done, exit MB.
Go to your local thumb folder, sort pictures by date, find those unwanted pictures and move them to another folder.
Go to the new folder with full of unwanted jpg files and create a batch file with a text editor as follows:
@echo off
:: Changes all jpg files in the folder to zero-byte files
for %%a in (*.jpg) do type nul>"%%a"
:: Changes file extension from jpg to pNg
ren *.jpg *.pNg
:: Moves the zero-byte files to the thumb cache folder (modify the target path to your own)
move *.pNg C:\MB\AppData\InternalCache\ArtistThumbs
As commented within the code, what it does is to change all jpg files to zero-byte png files and move them to your thumb cache folder, overwriting existing files.
It uses pNg rather than png as extension so that you can easily tell the file was created by you, not by MB.
Now if you re-start MB, it won't send a single request for a thumb for those artists as long as you keep that zero-byte file in the cache folder.
Also you can freely paste your own picture to those artists manually whenever you find a good thumb. Then the zero-byte file gets replaced by the local picture, so nothing to worry about.