1Score both sides of steak in a diamond pattern by making shallow diagonal cuts at 1-inch intervals. Place steak in a resealable plastic bag set in a shallow dish.
2In a screw-top jar, combine salad dressing, lime peel, lime juice, and cilantro. Cover and shake well. Pour half of the salad dressing mixture into a small bowl and add onion; cover and chill until serving time. Pour the remaining salad dressing mixture in jar over steak in bag. Seal bag; turn to coat steak. Marinate in the refrigerator for 24 hours, turning bag occasionally.
3Drain steak, discarding marinade. Sprinkle steak with salt and black pepper. For a charcoal grill, place steak on the rack of an uncovered grill directly over medium coals. Grill for 17 to 21 minutes for medium doneness (160°F), turning once. (For a gas grill, preheat grill. Reduce heat to medium. Place steak on grill rack. Cover and grill as above.) (To broil, place steak on the unheated rack of a broiler pan. Broil 3 to 4 inches from the heat for 15 to 18 minutes for medium doneness [160°F], turning once.)
4To serve, thinly slice steak across the grain. In a large bowl, toss together steak, salad greens, red pepper, avocado, and reserved dressing mixture. Fill each pita half with steak mixture.