Put about 2/3 of the whole garlic in a small bowl, add a little salt, and chop. Add 1 tablespoon thyme, chili powder, sugar, 1.5 tablespoons salt, and 2 teaspoons ground black pepper. Place the beef steaks on a baking sheet and grate with a hot mixture, cover and refrigerate for at least 4 hours, or better for a day.
In a separate bowl, combine tomatoes, onions, bell peppers, olive oil, vinegar, 1/4 cup water, leftover garlic, 1 tablespoon thyme, 2 teaspoons salt, and 1 teaspoon ground black pepper. Stir well, close tightly and refrigerate (this salsa can be prepared up to 24 hours before serving).
Turn on the grill until it reaches medium-high heat. Place the steaks on the grill rack and grill the beef steaks for about 4 minutes on each side, then cover the grill and grill the beef steaks for another 6-7 minutes on each side until the desired degree of doneness is desired.
Transfer the steaks to a cutting board, cover with foil, and set aside for 5 minutes, then cut into slices, place on a serving platter, and drizzle with salsa.