From their FAQ:
iBoostUp fails to launch after an update with error "iBoostUp is damaged and can't be opened"
We've had intermittent reports of this occurring with our 3.1 and 3.2 updates.
This issue is not specific to iBoostUp and related to a problem with the App Store itself.
To resolve, please:
Remove iBoostUp from your Applications
Remove com.ituneup.ituneup.plist and com.ituneup.ituneup.plist.lockfile from ~/Library/Preferences
Download iBoostUp from the Mac App Store
In case you are unable to locate the above-mentioned files please try the following:
Open Terminal.app from Applications -> Utilities
Type "rm ~/Library/Preferences/com.ituneup.*" without quotes and then hit [enter]
Re-download iBoostUp again from the app store.
To re-enable any of your previous purchases please follow the steps in FAQ entry #12