Add the squid to a non-metallic bowl with 1 1/2 tablespoons olive oil, the garlic, chile, and toss to coat the squid. Cover the bowl with plastic wrap, and leave it in the refrigerator to marinate for 2 to 3 hours.
Heat a large frying pan over high heat. Remove the squid from the marinade, and discard the marinade. Add the squid strips, and cook until it is just cooked, about 1 to 2 minutes per side. Take care not to overcook the squid or it will become tough.
Combine the cucumber, tomatoes, celery, celery leaves and basil in a large bowl.
In a separate bowl, whisk together the remaining 1 tablespoon olive oil and lemon juice, and season the mixture with the sea salt and black pepper. Set the dressing aside.
Add the squid to the vegetables and toss well. Pile the salad onto a large platter, garnish with the capers and drizzle with the lemon dressing. Serve the salad immediately.