Soak the toothpicks in a bowl of water for at least 1/2 hour.
Clean the calamari thoroughly. Be sure there is no gristle or ink left inside.
Stem and wash the spinach. Make sure all the sand is removed. Chop the garlic finely. In a large sauté pan, heat the olive oil over low heat. Add the garlic, and make sure it does not burn. Add the spinach and salt to taste and sauté over low heat until it is thoroughly wilted. Drain well. Chop finely.
Put a small amount of the filling (about 2 tablespoons) into each squid body. Secure the top with a toothpick.
Brush both sides with olive oil.
Grill over hot grill (or in a grill pan) for about 4 minutes on each side.