Rinse the olives under cold water to remove excess saltiness. If using anchovy fillets, rinse and pat them dry.
In a food processor, combine the pitted olives, capers, minced garlic, anchovy fillets (if using), and fresh lemon juice. Pulse until the ingredients are finely chopped and well combined, but not completely smooth.
With the food processor running, gradually drizzle in the extra virgin olive oil until the mixture becomes a thick paste. Taste and season with freshly ground black pepper as needed. Adjust the saltiness if necessary, keeping in mind that the olives and capers already provide saltiness.
Transfer the tapenade to a serving bowl and stir in the chopped parsley. If desired, drizzle a little extra olive oil over the top. Serve the tapenade dip with crackers, bread, or pitta.