Combine 1 cup of the garlic salsa with the vinegar, oregano, sugar, and salt in a resealable plastic bag. Add the steak and marinate 30 minutes or up to 4 hours.
Light a charcoal grill and allow the coals to burn until covered with gray ash or heat a gas grill to high.
Remove the beef from the marinade and cook 3 to 4 minutes, turn, then cook 3 to 4 minutes more or until medium rare. Slice thinly against the grain. Pile slices on the Rosemary Flatbread and serve with the remaining salsa.