I got the request from the customer to remove the stain from the backsplash. This made me thinking: how to keep poultice on the stain and prevent from coming down?

The stain was made by varnish used to refinish kitchen cabinets. Material - honed travertine, sealed prior to staining. Mineral spirits or goof off cleaned up just a little from the surface but it seams stain penetrated the surface of the stone. Stone was sealed before the staining.