I checked a lot of things, also tried to change gamma of the bump texture, not sure if I did it correct. In 3ds Max when you are loading a bitmap, you can either use gamma 2,2 or override it to custom value. For bump maps, it is recommended to use gamma 1.0. I nested the bitmap into "layer" and then changed gamma to 0,454 , no effect though... Maybe someone who knows C4D better could check if changing gamma has any impact on this?
I only discovered that lowering glossiness value of the material seems to help, but it looks like the bumped reflection is incorrect anyway.