Cook the rotini pasta according to package instructions until al dente. Drain and rinse under cold water to stop the cooking process. Set aside to cool.
In a large mixing bowl, combine the drained tuna, mayonnaise, Greek yogurt, and lemon juice. Stir until well mixed.
Add the diced celery, red bell pepper, red onion, sweet pickle relish, and fresh parsley to the bowl. Mix until the vegetables are evenly distributed.
Once the pasta has cooled, add it to the tuna mixture. Gently fold the pasta into the salad until everything is well combined.
Season with salt and pepper to taste, adjusting as necessary. If the salad seems too thick, add a little more Greek yogurt or a splash of water to achieve your desired consistency.
Cover the bowl and refrigerate for at least 30 minutes to allow the flavors to meld together before serving.