If I remove a pico from the Lutron app it still shows in button controller. If I rename a pico in the Lutron app the old name is still used and the new name does not show up in button controller.
To get rid of an old pico I had kill both apps and do a complete new install and config.
If you removed the device from the Lutron Integration app, that does not remove the virtual device that was created before. You have to manually remove that device yourself. Did you do that?