Trim fat from steak. Combine seasoning ingredients; press evenly into both sides of beef steak. Place steak on rack on broiler pan so surface of beef is 3" to 4 " from heat. Broil approximately 15 to 20 minutes for medium-rare (145 degrees F. internal temperature) to medium doneness (160 degrees F. for internal temperature), turning once.
Meanwhile, combine relish ingredients; set aside.
Carve steak into thin slices. Arrange equal amounts of beef on top of each pita; top with relish and cheese. Serve with a cucumber salad and a side of grapes.