Trim fat from steaks. Cut each steak in half.
In a large heavy skillet melt butter over medium-high heat.
Add steaks; reduce heat to medium. Cook for 10 to 12 minutes for medium-rare (145 degree F) to medium (160 degree F) doneness, turning once.
Transfer steaks to a serving platter, reserving drippings in skillet.
Cover steaks; keep warm.
Stir green onions, thyme, salt, and pepper into reserved drippings in skillet.
Cook for 1 to 2 minutes or until green onions are tender.
Stir in tomato; heat through.
Serve tomato mixture over steaks.