@alex1223 - If you’ve already adjusted the monitor brightness to it’s lowest level then you’ve got a problem. You may be able to adjust the contrast to increase it. That should make the gray/white pop a bit more, but if you’re seeing the back light then it won’t help all that much.
Unfortunately, the only solution I can think of is to replace your mirror glass with a variant that lets in less light. You can purchase samples of different one way glass recipes and hold them up to the monitor to find one that reflects enough light that the back light isn’t visible. It will limit how bright the white is, of course.