Mix tomatoes, mozzarella, basil, 1 clove minced garlic, and 1 tablespoon olive oil in a bowl; toss to coat. Cover bowl and refrigerate.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Place steak in a large resealable bag; add 1 clove minced garlic, 1 tablespoon olive oil, salt, and pepper. Seal the bag and distribute the oil mixture over the steak.
When the grill is preheated, cook steak to your desired degree of doneness, about 5 minutes per side for medium. An instant-read thermometer inserted into the center should read 140 degrees F (60 degrees C). Let stand for 5 minutes before thinly slicing across the grain.
Divide lettuce onto 4 serving plates. Drizzle 1 ½ teaspoons each of balsamic vinegar and olive oil onto each lettuce portion. Divide steak and tomato mixture evenly between the salads.
