Noise left on texture when cleared (fog of war, Shader)

Hi everyone, so I'm trying to do a fog of war, I managed to have a fairly satisfying result as follows:

The black fog covers everything and is removed definitively, and the grey fog remains and only shows my units. The only problem is that when I move the units, there is residue on the right and left as we can see in this screenshot :

what's creating it ? How to deal with this problem?