In a small bowl, blend olive oil, vinegar, mustard, 1 teaspoon of the Greek seasoning and brown sugar. Reserve 3 tablespoons of the mixture. Place the remainder in a large resealable plastic bag. Add the steak and marinate in the refrigerator for one to 4 hours.
In a second small bowl, mix together the yogurt and feta; cover and refrigerate until ready to use.
Heat gas grill to medium-high or coals in charcoal grill to medium hot. Lightly coat grill rack with oil or cooking spray.
Brush tomatoes and onion with some of the reserved oil and wine mixture. Place tomatoes on grill, cut-side down along with onion slices. Grill for 3 minutes; turn, brush with remaining oil mixture and grill tomatoes for additional 2 minutes and onions for 3 minutes, until tender. Remove to a plate and keep warm.
Remove steak from resealable bag and grill about 2 minutes per side or until internal temperature reaches 130 degrees F on an instant-read thermometer for medium-rare. Remove from grill and allow to stand 2 minutes before thinly slicing.
Serve pita slightly warmed and layer with lettuce, yogurt mixture and sliced steak. Accompany with grilled tomatoes and onion.