Rub steaks with olive oil and season to taste with salt and pepper. Prepare a charcoal or gas grill for very high heat (600°; you can hold your hand 5 in. above cooking grate only 2 to 4 seconds). While grill heats, preheat cooking grate for at least 10 minutes.
Meanwhile, warm 4 dinner plates. Put marinara in a small saucepan and stir over medium-high heat until simmering, about 3 minutes; keep warm.
Grill steaks, turning over once, until rare in the center (cut to test; meat will continue to cook after coming off the grill), 2 to 3 minutes for medium rare. Skirt steaks may need 2 to 3 minutes longer than New York steaks. Lift steaks to a platter.
Quickly spoon marinara over center of each plate. Set steaks on marinara, arrange mozzarella slices on steaks, and mound arugula on cheese. Pour meat juices from platter over salads if you like.
Note: Nutritional analysis is per serving.