In a large pasta bowl, break up the tuna and set aside. Heat the extra virgin olive oil in a large skillet over medium heat and add the garlic. Cook, stirring, just until fragrant, and add the Marinara sauce. Stir in the olives, season to taste with salt and freshly ground black pepper, and let it simmer for 5 minutes.
Meanwhile cook the Tagliatelle according to package directions and drain, reserving 1/2 cup of the pasta cooking water.
Add the Tagliatelle to the Marinara sauce and toss, adding pasta water a little at a time to loosen the sauce if necessary. Remove from heat and add to the tuna. Add the chopped parsley and the capers, and mix together. Divide the Tagliatelle among plates and garnish with the burrata and more parsley, if desired.