Pulse nori in a blender until it's a fine powder. Set aside to let dust settle.
Mash chickpeas with a sturdy fork or a small-holed potato masher (chickpeas slip through larger, zigzag-type mashers) in a large bowl until most are broken up. Do not overmash--they should retain some texture.
Stir in mayo and mash a little more. Stir in nori powder, carrot, celery, onion, dill, salt, and pepper. Cover and chill at least 15 minutes or up to 3 days.
For the sandwiches, slather toast with mayo (about 1 1/2 teaspoons per slice). Layer salad, lettuce, and tomato between toast slices. Cut sandwiches in half diagonally.