Soak skirt steak in water for a few hours or overnight, to remove some of the saltiness. Pat dry. In a small bowl, combine the red wine vinegar, olive oil, crushed garlic, salt and pepper. Set aside. Heat a large dry skillet over medium heat. When you feel the heat rising from the pan, add 1 tablespoon of  olive oil. Cut the steak as necessary to fit into the pan. Sear skirt steak, 5 minutes per side for medium, or until desired doneness, in batches as necessary. Transfer steak to cutting board and let rest 5 minutes.

Using the same pan, sauté the sliced mushrooms in the remaining 2 tablespoons of olive oil for 2 minutes. Slice steak on slight diagonal, across the grain, in ¼ inch slices. Arrange romaine lettuce greens on 4 dinner plates. Top with sliced red onion, sautéed mushrooms, and halved grape tomatoes. Drizzle a bit of dressing over each salad. Garnish with sliced steak.