Preheat grill to 350°F or medium high temperature.
In a bowl toss shrimp with 2 tablespoons olive oil, salt and pepper. Set aside.
To make gremolata, combine lime zest and juice, cilantro, garlic, okra and jalapeño in a food processor bowl. Pulse until just combined and still slightly chunky. Pulse more if you prefer a finer texture.
Pour gremolata into a serving dish and fold in remaining olive oil until smooth. Season as needed to taste and set aside.
Grill shrimp 2 to 3 minutes per side or until just pink and curled into a "c" shape.
Plate and drizzle with gremolata. Season to taste as needed.