Okay, your eyes see everything? Correct? Your brain recieves the signals? Correct? Now you use your brain to divide the two layers (1 is the reflection, 1 is the actual image on the screen). Now you only focus on the screen one. If people want to test this, hold your finger in front of your eyes and focus on a object which is about 60-70 cm from you and behind the finger. Even with a finger you see most of the object behind, but since the finger is solid you never really "do not see it".
We do not see EVERYTHING in our vision field, we see what we focus on, the rest is just something blurry until we focus on this. And since the actual reflection is not solid you barely even notice it.
I been doing this with everything, even the old CRT screens with light from big 3 meter wide windows it works for me, only annoying part then is that you see the dust more in the light.
Just use your brain, it's the most powerfull machine in the world, so why not make use of it?