I have been keeping a battery tender attached to the battery to keep it charged since I don't use the van much. But now when I turn the engine off and remove the key I noticed that the green illumination on the stock radio LCD panel is lit, the radio is off the LCD readout is off but the green illumination only for the LCD panel remains backlit anywhere from a 1 to 10 minutes. Important to note its not the illumination that lights the buttons when you turn the headlights on.

Can damage occur from using a tender?