First, make sure that the information stored in iTunes is also stored in the music files and not just in the iTunes database.
(I think that iTunes saves all the information in the files if you modify the tag version e.g. from 2.3 to 2.3).
Also check the web for utilities that do just this for the covers.
see e.g. this thread: /t/11271/1
and also this German thread which has a couple of links to utilities in it:
https://forums.mp3tag.de/lofiversion/index.php?t9424.html
Apparently, the "itsfv Tool" is the thing to look for.
Mp3tag will not go through your library and update anything unless you tell it to do so.
MP3tag does also not guess what might be the more correct data. You are in command.