Our sea vegetables are sometimes rinsed or soaked in fresh water before use, but often this is unnecessary. Dulse, for instance, is eaten right out of the bag as a healthy, "salty" snack. Kelp is often lightly soaked and rehydrated (it expands!) to be cut into attractive shapes and sizes. In any case, a light rinse before use lessens sea vegetables' salty taste. You will lose some sodium and potassium salts, but very little if any calcium, iron, magnesium, etc. You can save the rinse water for cooking.  It is not a good idea to rinse sea veggies and then store them, unless you're going to use within 24-48 hours or refrigerate.
You may want to inspect the plants for tiny shells (periwinkles) before use. We do our best but sometimes they hide in the folds. Simply dip the plants in water long enough to unfold them and release any shells.