mr. clean
Its not a panacea, but Mr. Clean magic eraser works well in some cases...sort of like cleaning the ceiling of the Sistene Chapel, but worth a try. Works on topical (bottomical, since its the underside?) soiled areas only, not bleed-thru stains. I'd then use a clean micro-fibre cloth after. If you are going to use something like the SEM product, you want that surface as clean as possible...washing and rinsing are sort of difficult, so the eraser is a good option. You might call the SEM folks; they have been helpful in the past to me.