DO-AHEAD TIP: Marinate steaks overnight or for at least 5 hours (see recipe).
Prepare marinade: In a small bowl, whisk together vinegar, olive oil, 2 tablespoons of lime juice, garlic, and tomato paste.
Season steaks with salt and pepper and place them in a large zipper-topped plastic bag; pour marinade on top. Seal bag and turn to coat; refrigerate overnight or for at least 5 hours.
Preheat outdoor grill to MEDIUM-HIGH. Remove steaks from marinade, discarding marinade and bag. Grill steaks for 3 to 4 minutes per side or until desired level of doneness is achieved; transfer steaks to a cutting board and allow them to rest for 5 minutes.
Meanwhile, place diced avocado and halved cherry tomatoes in a large bowl; add remaining 2 tablespoons of lime juice and salt and pepper to taste.
Slice steaks into bite-sized cubes and add to avocado/tomato mixture; toss well and serve.