Apple - How to remove apps that are remembered by App Store?

This will not be possible. You will see an cloud icon when you previously "purchased" an app. This will notify you that you could download the app without any costs.

It is not possible to delete those apps from your Apple ID.

If you don't want to see the cloud icon, you could sign out from the appstore via settings > iTunes & App Store > sign out. This will hide the cloud icon but you have to log in each time you want to download an app.

You can delete the apps from your local iTunes, but they will show in your 'Purchased' view. If you don't want to see them any longer, you can simply right click and choose 'Hide'. They won't show in your Purchased view.

If you want to hide an app on an iPod 4, iPhone 4 or a newer model of either you just have to go to "purchased" in the App Store app and slide the app to the left, then click "hide".