I'd dump it Franny. I think when Jo gives the dog a bath in the back room where my tanks are, that when she blow dries her, crap gets in my tanks. Shampoo is a soap. I don't think detergent is good for the water quality. When the groomer comes over, we drape plastic over the tanks to keep the shampooed, blown dry hair from getting in the tanks.
You don't know what all may be in the dust particles that got into the holding tank. Coming from a bathroom...detergent, grout, glue, all sorts of things could be introduced.
I would just go ahead and make the precautionary steps to be safe.
On another subject, kinda. Do you add anything to your holding tank? Or do you just let the water age in it?