Combine beef, tomatoes, lemon or lime peel, salt, and pepper in a medium bowl; mix lightly but thoroughly. Shape into eight 1/2-inch-thick patties. Grill patties on the rack of an uncovered grill directly over medium heat for 14 to 18 minutes or until an instant-read thermometer inserted in side of patty registers 160 degrees F., turning once.
Meanwhile, combine the light mayonnaise or salad dressing, basil, and jalapeno peppers in a small bowl; mix well. During the last 1 to 2 minutes of grilling, place buns, cut sides down, on grill rack to toast. Place burgers on bottom halves of buns. Top with the mayonnaise dressing mixture and arugula or spinach. Add the bun tops. Makes 8 servings.