This is an interesting topic. The window screen we have here blocks about 25% of the light, brand new out of the package. I use a double layer of this material as 50% shade cloth for a growing area outside. To get those numbers I use a light meter, which I would recommend if anyone is curious about the exposure in different situations. They're not expensive and I was surprised by what I learned.
More than anything else in my experience, simply washing the window improves light transmission tremendously. Presumably you could also clean the screen. Dust and dirt tends to accumulate in the space between the window and the screen, more than anywhere else. One of our kitchen windows here is half screened (perfect control), and has never been cleaned outside, and that screen blocks 40% of the light.
I suspect the difference between 25-40% (my figure) and 40-70% (Gene's figure) may have to do with the material the screen is made from, or perhaps simply it represents the varying accumulation of dust in all the nooks and crannies over time.
