You can install a 1/8W or 1/4W resistor inline on the illumination terminal on the backside of the remote to dim the brightness to a desired level. Go to RadioShack and buy a small variety pack of resistors and try different ones till you find your liking luminance.
When the sun is on the remote's LCD, the brighter the display, the more legible it is during the day so if you put a resistor inline, you may cut down your daytime visibility in direct sunlight.
If you want to be trick, follow the diagram attached and have the best of both worlds.

According to Clarion, this has been address in the new products coming out.