My first thought was “opposition effect,” but I believe that only occurs directly opposite the light. In other words, if the moon was high off your left, then you’d witness the opposition effect low on your right like a spotlight. It happens because you’re in line with the light source and the stuff that is illuminated on that axis hides its own shadow. It makes that spot look brighter and the surrounding area look darker. If I’m understanding the situation, the light appeared on the ground in the direction of the moon, so opposition effect doesn’t seem to be the answer.
My second thought is that I’m somehow on the right track but don’t have time to give it much thought at the moment! Perhaps something like specular reflection, but I thought that that only happened with very reflective surfaces. Then again, maybe you’re talking about very reflective surfaces…
Can you guess at where you saw the light on the ground… the moon-earth-eye angle?
Dave