MacOS – How to stop iTunes from automatically re-downloading

Is there a Downloads item in the Store area of the column on the left side of iTunes? If so then you can click on it, click on the stalled download, and delete it.

Edited to add

There are a couple of places you might check after quitting iTunes. The first is

/Users/yourUserName/Music/iTunes/Mobile Applications/Downloads/

Make sure it's empty, and if not, remove what's in there (set it aside so you can put it back if it confuses iTunes later).

The other place is:

/Users/yourUserName/Music/iTunes/Mobile Applications/

and look for the file Dexter.ipa (or DexteGame.ipa or whatever the game is called). Delete this file -- it's the actual now-outdated game that iTunes is trying to update.

Otherwise iTunes has the need to download it stored in its database and doesn't care about files.

I take it that agreeing to the download doesn't help?

Mac Answer:

You can disable device backups with this terminal command:

defaults write com.apple.iTunes DeviceBackupsDisabled -bool true

More info here.