The soap is formulated to sheet like that to aid in the spot free drying; apparently it is a polymer soap that treats the surface so that the water sheets. The thing that bothered me about the system was how filthy (almost black) my wash mitt became when using that soap. I'm not sure what causes that, but I have seen other people mention the same thing. To answer your question I don't *think* it will strip off your Zaino, but I just don't care for the soap.
I really only bought it for the filtered rinse, but I tried using the soap a couple of times. It then got to the point that if I used that system at all, it was just for the spot free filtered rinse. Then I realized that if I used the "sheeting" method to rinse, that I could dry it a lot faster than messing with that thing.
If it works for you that is great, but I feel a lot better using my foam gun, a trusted soap, and a rinse bucket w/grit guard for my sheepskin mitt.