How do I stop MacAppStore from showing updates for deleted apps? I've deleted apps that were purchased through the Mac AppStore. I used "CleanApp" to delete the parts left in app support folders.

But I still see notifications of updates in the AppStore app.

I know I can hide the app name in the Purchases tab, but is there any way to remove these notifications permanently?

It is not just a cosmetic thing. If I have multiple updates and I select "Update All Apps",  the deleted apps will be reinstalled.

Please note I am asking about the Mac App Store, not the iOS Store.
Usually this is a problem with spotlight.

The simplest step is to shut down the mac, disconnect all external drives, and start up to make sure no extra volumes are mounted. The next step would be to rebuild the spotlight index.

Lastly, search in other user accounts to be sure another user didn't somehow install or copy that App into their home folder.