In a wide, shallow bowl, whisk 1/4 cup artichoke marinade (discard remainder or save for other uses), vinegar, mustard, and garlic.
Rinse and drain fennel. Cut off and save a few feathery green leaves for garnish. Trim off and discard remaining stalks, root end, and any bruised areas. Cut head in half lengthwise across widest dimension, then cut each half crosswise into paper-thin slivers.
Add fennel, tomatoes, olives, basil, onion, and artichoke hearts to dressing in bowl. Mix gently to coat. Garnish salad with reserved fennel leaves. Add pepper to taste.