Place each piece of pork between 2 sheets of heavy-duty plastic wrap, and pound each piece to 1/4-inch thickness using a meat mallet or a rolling pin.
Combine 2 tablespoons vinegar, juice, thyme, salt, and pepper in a small bowl. Reserve 1 tablespoon juice mixture.
Pour the remaining juice mixture in a large zip-top plastic bag.
Add pork; seal and marinate in refrigerator for 1 hour, turning occasionally.
Preheat grill to medium heat.
Place peaches, cut sides up, on a plate; drizzle with remaining 2 tablespoons vinegar.
Place pork on grill rack coated with cooking spray; grill 3 minutes on each side or until pork is done. Set aside.
Place peaches, cut sides down, on grill rack; grill 4 minutes or until soft and slightly browned. Turn and cook 2 minutes or until heated through.
Cut each peach half into 4 slices. Slice pieces of pork into 1-inch-thick strips.
Drizzle trimmed arugula with reserved 1 tablespoon juice mixture, tossing to coat. Divide arugula evenly among 4 plates. Top with grilled pork strips and peach slices; sprinkle evenly with turbinado sugar.
