For LCD screens it doesn't matter. They use the same amount of power whether the screen is black or white. There's no way to damage the screen by displaying an image.
OLED displays are vulnerable to burn in. So a bright static image left on screen for a long time can result in a latent image that's permanently burned into the screen. That's because the OLEDs degrade faster when they're brighter. But a black screen should have no effect.