Sprinkle the steaks with 1-1/4 tsp. salt and 2 tsp. pepper.
In a medium bowl, mix 4 Tbs. oil with the soy sauce, 3 tsp. thyme, the Worcestershire, mustard, vinegar, and garlic. Put the steaks in a large bowl and coat them with the soy sauce mixture. Cover the bowl and marinate the steaks in the refrigerator, turning occasionally, for at least 4 hours and up to 1 day.
For a gas grill, light the front burner to medium-high and the back burner(s) to medium-low. For a charcoal grill, light a medium fire (about 300°F to 350°F) with two-thirds of the coals banked to one side. Clean and oil the grill grates. While the grill heats, set the steaks out at room temperature. Toss the scallions with the remaining Tbs. oil and 1/2 tsp. each salt and pepper.
Set the steaks over the hotter part of the fire and the scallions over the cooler zone. Cook, covered, until the scallions brown, about 3 minutes, and the steaks have good grill marks and easily release from the grate, about 4 minutes. Flip both the scallions and steaks. Cook the steaks until they’re just firm to the touch, pink when you slice into a thicker part, and register 135°F on an instant-read thermometer for medium-rare, about 4 minutes. Grill the scallions until browned and softened, about 3 more minutes.
Transfer the steaks to dinner plates, top with the remaining tsp. thyme, and serve with the scallions.