Bring a large pot of salted water to a boil and cook tortellini according to package instructions until al dente.
Drain the cooked tortellini and immediately rinse with cold water to stop the cooking process; drain thoroughly.
In a large mixing bowl, combine the cooled tortellini, halved cherry tomatoes, sliced cucumber, diced red onion, and diced bell pepper.
Add the sliced olives and crumbled feta cheese to the bowl.
In a small container, whisk together the Italian vinaigrette and dried oregano.
Pour the dressing over the salad and toss gently with a spatula until all ingredients are evenly coated.
Garnish with chopped fresh parsley.
Cover and refrigerate for at least 30 minutes prior to serving to allow flavors to meld.