Drain bocconcini, reserving 1/3 cup marinade. Combine reserved marinade and vinegar in small bowl. Toss zucchini and bell pepper with 2 tablespoons marinade mixture in large bowl; cover and refrigerate until ready to use. Place beef Strip Steaks Boneless and remaining marinade mixture in food-safe plastic bag; turn steaks to coat. Close bag securely and marinate in refrigerator 15 minutes to 2 hours.
Remove steaks from marinade; discard marinade. Remove vegetables from marinade; place in grill basket. Place steaks on one half of grid over medium, ash-covered coals; place grill basket on other half of grid. Grill steaks, covered, 7 to 10 minutes (over medium heat on preheated gas grill, times remain the same) for medium rare (145°F) to medium (160°F) doneness, turning occasionally. Remove steaks; keep warm. Grill vegetables 10 to 13 minutes or until crisp-tender, stirring occasionally. Add tomatoes during last 2 minutes of grilling.
Combine grilled vegetables and bocconcini in large bowl; toss gently to combine. Carve steaks into slices; season with salt, as desired. Serve with vegetable mixture.
Nutrition information per serving: 380 Calories; 189 kcal Calories from fat; 21 g Total Fat; 12 g Saturated Fat; 3 g Monounsaturated Fat; 106 mg Cholesterol; 152 mg Sodium; 8 g Total Carbohydrate; 1.8 g Dietary Fiber; 38 g Protein; 2.4 mg Iron; 8 mg NE Niacin; 0.8 mg Vitamin B6; 1.4 mcg Vitamin B12; 4.9 mg Zinc; 29 mcg Selenium;