Crepe myrtle bark scale 'soot' removal

I have a client with several beautiful crepe myrtles which had the heaviest infestation of CMBS last year that I had ever seen. I treated with imidacloprid drench which seems to have worked. I don't see any scale bodies on the trees. Not unexpected, the 'soot' discoloration from last year is still present. My understanding is that this black material is fungal overgrowth on the 'honeydew' produced by the scale insects.

I know that this will eventually go away. But, aside from scrubbing...

Crepe myrtle bark scale 'soot' removal