Impossible
Sadly, what you're describing would be impossible. A reflection is just a more uniform way that light bounces off an object. As the person can be seen, light resembling their image is travelling away. If it interacts with any surface that can cast a reflection, it'll be a reflection.
You could go a technobabble way. Light can interfere with itself. You could say that any light that is coming off the person is detected, then some other light is generated to interfere with those specific particles. They could then make the light of the person fly away in a random direction. That will make the reflection next to nothing compared to the 'background' light.
It is technobabble as it is incredibly difficult to do. It is safe to say that isit is so difficult as to be impossible, even if you knew where each photon is. As it is light, it is impossible in practice to detectzdetect, track, and counteract each photon. This is magic territory.