Boil pasta in salted water, according to package directions. Reserve ½ cup pasta water, then drain.
Chop garlic. Sprinkle with ¼ teaspoon salt and make a paste by dragging the blade of knife across the mixture.
Add garlic paste to a small bowl. Mix with mayonnaise, mustard, lemon zest. lemon juice and artichoke marinade. Whisk to combine and season with salt and pepper.
Return cooked pasta to pot. Add artichokes, olives and dressing and toss, adding enough pasta water to create a light sauce to coat. Stir in Parmesan cheese and season with salt and pepper, to taste.