Toss grapes with olive oil and balsamic vinegar. Place on jelly roll pan and roast for 10 minutes. Remove from oven and place in a small bowl being sure to get the juices, too. Add walnuts, lemon juice, salt, and pepper. Toss gently to coat.
Place arugula in a salad bowl and add the the roasted grape and walnut combination and toss to combine. Sprinkle with feta cheese and serve.