Heat gas or charcoal grill for indirect grilling as directed in owner's manual. Cut two 12-inch square pieces of heavy-duty foil. In small bowl, mix tuna, onion, bell pepper and pickles. Stir in mustard and cheese.
Spoon tuna mixture on 2 bread slices; top with remaining bread slices. Place each sandwich on center of foil piece. Fold foil over sandwich so edges meet. Seal edges, making tight 1/2-inch fold; fold again. Allow space on sides for circulation and expansion.
Place packets over unheated area on grill. Cover and grill 12 to 15 minutes or until sandwiches are heated through.