Whisk steak sauce, vinegar and oil until blended. Pour 1/4 over steak in shallow dish; turn to evenly coat both sides of steak. Refrigerate 1 hour to marinate, turning after 30 min.
Heat grill to medium heat. Remove steak from marinade; discard marinade. Grill steak 6 min. on each side or until medium doneness (160ºF). Bring remaining steak sauce mixture to boil in saucepan on medium heat; simmer on low heat 1 min.
Cut steak across the grain into thin slices. Toss salad greens with tomatoes, cucumbers and meat in large bowl. Add steak sauce mixture; toss to evenly coat. Top with cheese.