I am not an expert on this as with shellfish I have always expected a bit of grit. But the procedure I have always been taught and practice is to start as @FuzzyChef says, brush the exterior in running water to get that grime off.
Then you are trying to purge, not store, so purge them in fresh water, not salt. They are a salt water creature, not fresh, so long exposure to fresh water will kill them, but you are not giving them long exposure, you are giving them short. Over a short time, fresh water is an irritant for them and the theory at least is they respond by purging to get rid of it, and with it the sand and such that have in their lining or at least a good part of it. If on the other hand you use salt water, you reduce this irritate, or match their living ratio which make them happy and they wont purge. Or if you go way over, well you are creating a solution that at best matches the effect of fresh water but leaves you with an overly salty product, or worse kills them before they can purge.