Drain the canned chicken thoroughly in a colander, then transfer to a large mixing bowl. Use a fork to break it into small flakes.
In a separate small bowl, whisk together mayonnaise, Greek yogurt, Dijon mustard, and lemon juice until completely smooth.
Add the halved grapes, diced celery, chopped red onion, walnuts, and parsley to the bowl with the chicken.
Pour the dressing over the chicken mixture. Using a rubber spatula, gently fold everything together until evenly coated.
Season with salt and pepper, then taste and adjust if needed. Cover and refrigerate for at least 30 minutes before serving to allow flavors to meld.