To put it another way, only 7% of the sunlight that hits the moon gets reflected. But of that 7%, only a tiny portion gets reflected such that it intersects with the earth since it is radiated in all directions, so we only capture a very tiny percent of that 7%.
By analogy, it would be the difference in light between staring into a flashlight at night and seeing the light of that same flashlight reflected off a not-particularly-reflective distant object.
And yet, on a clear enough night, one can see the filled-in outline of the circle on the dark side of a crescent moon. The area beyond the terminator is shining by ... reflected Earthshine. This is VERY dim, but often noticeable.
Which is to say you have an object (Earth) shining by reflected sunlight. We know from photographs taken on the moon thirty years ago that it is glowing as a big blue ball in the Lunar sky. Some little bit of that light finds its way back to Earth.
The distances involved and the inverse square law dictate that the losses should be incredible. They are. Nevertheless, the original source, the sun, is bright enough that you can still see SOMETHING brighter than the background on the dark side of a crescent moon if you look closely on a very clear night.