Cut the squid bodies along the sides so they lay flat.
In a bowl combine the olive oil, juice of one of the lemons and the rest of the ingredients, except the parsley.
Add the squid, toss to coat and refrigerate for 2 hours, tossing every 30 minutes or so, to make sure the marinade gets evenly distributed.
Preheat the grill to high. Place a piece of foil on the grill and brush it with a light coating of vegetable oil to keep the squid from slipping through the grill grates and sticking to the foil.
Grill the squid, about 3 – 4 minutes per side, until it turns opaque. Remove from the grill, garnish with the fresh parsley and the remaining lemon, cut into wedges.