How do I permanently delete a previously downloaded iPhone app so that it no longer appears in my list in iTunes?

Are you referring to the Purchased List, or just appearing as installed? Hide and unhide purchases in the iTunes Store - Apple Support

You can delete it from the device, or delete it from iTunes. Deleting it from the device will remove it from the device. If you delete it from iTunes, then it will also not try to sync again the next time you sync the device.