iTunes is able to accommodate more than one image for a track entry's artwork. What hasn't always been obvious is that the first artwork in an array of artworks in a track is the "display" artwork. Any additional artwork in the artworks array are spares. Modern versions of the iTunes Get Info Artwork panel now label images as "Album Artwork" and "Other Artwork".
Some people think that these "Other Artwork" have to go.
It is a simple matter to simply remove the other artwork from a track entry with an AppleScript. Here's one now that goes through each track in a selection and repeats through its artworks (if there's more than one artwork), removing the last artwork until there is only the first one left:
tell application "iTunes"
set selectedTracks to selection of front browser window
repeat with i from 1 to (count of selectedTracks)
set thisTrack to item i of selectedTracks
if (count of its artworks) > 1 then
repeat until ((count of its artworks) is 1)
delete its last artwork
Click the script icon above to download this script to Script Editor at your house and click "New Script" to allow it to open. Save it named whatever you like in your ~/Library/iTunes/Scripts/ folder (or wherever you put them). Select some tracks in iTunes and launch the script.
There's always the kid in the front who wants to know why you don't make a script like this that just works on the entire library. Well: iTunes can be kind of touchy when AppleScripting a large amount of artwork stuff. It may "go modal" as it updates its database and under such circumstances may block an AppleScript from continuing its operation. So I purposely used the selection object so that the script can be used piecemeal on a small batch of tracks at a time. Additionally, you might want to eyeball the "Other Artworks" of a track before you start blindly mowing them all down; in which case having to select the tracks manually compels you to be in control.
The routines are in a try block to skip over errors because of what I mentioned above about modality and also in case there's some image gunk in there that causes trouble. Because images downloaded from the internet that you use as album artwork are always pristine, right?