How can I permanently remove an app from the iPhone?

You might be seeing the data that the app stored in iCloud. It will remain there in case you want to use it on another device or redownload the app. You can delete the data that an app stores in iCloud by going to Settings > [name on top] > iCloud > Manage Account Storage.

App are never stored in iCloud. When you delete an app it does not remain in iCloud and never was in iCloud.

After you delete an app, if you reinstall it from the App Store you will see an icon that is a cloud with a down arrow. That only indicates that it is an app that you previously downloaded, not that it is in iCloud. If you reinstall it, it comes for the App Store, not from iCloud.

Jklxyz Said:

"iCloud apps: When I delete an app it remains in the cloud. How do I totally remove it?"

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Deleting this App:

You can't. Seems to me, you are looking to "Hide" the app from you purchases. If so...

1. Go Here: Lock or hide an app on iPhone - Apple Support
2. Scroll to: Hide an app
3. Proceed from there as necessary