The "Anytune damaged and can't be opened" message is provided by the operating system (specifically by Gatekeeper) when the file is suspected of being tampered with.
- Go to your Applications folder and move Anytune.app to Trash
- Open the App Store app and Download Anytune again
Normally, Apple will not allow you to purchase an app or in-app purchase if you already own it. You can download apps you purchased as many times as you want as long as you use the same AppleID. In this case, you should see download instead of purchase in the store.
Deleting Anytune (Applications/Anytune.app) does not delete Anytune's data including imported songs and config data (settings, marks, notes and lyrics).
In rare occurrences you may need to reboot your Mac, or even Sign Out, Reboot and Sign In to the App Store app before the App Store app realizes Anytune can be downloaded again.
- Open App Store app on your Mac
- Click your Name > View Information
App Store menu > Store
- Sign Out and Sign In
You may also need to restart you Mac while logged out of the store.
You could also try to disable GateKeeper:
Disable Gatekeeper from the Command Line
- Launch Terminal (/Applications/Utilities/) and issue the following command to turn off Gatekeeper:
sudo spctl --master-disable
- Hit return and enter the admin password as required by sudo, and Gatekeeper will instantly be disabled.
- Confirm the setting:
This will report back ‘assessments disabled’ to indicate that Gatekeeper has been turned off. You will also find that the Gatekeeper Security preference panel will be set to ‘Everywhere’.
How to Enable Gatekeeper from the Command Line
- Launch Terminal (/Applications/Utilities/) and issue the following command to turn on Gatekeeper:
sudo spctl --master-enable