So this is a tricky question because any strong cleaning products can remove the print of your Mighty Wallet but I've found a solution that seems to have the best effect with minimal abrasion and ink removal, Ethanol Wipes.
These are not the tiny packets that you sometimes get to "sanitize" your hands but I prefer the milder wipes that are used as flushable wipes or the Lysol brand cleaning wipes
Basically these can be found in any stores from Staples to Target to a grocery store but it's how you use them that's important. Gentle wipes seems to remove some of the grime but if you apply any force to the wallet you risk removing the inks especially in a custom print but less so on the standard designs that are offset printed.