First, prepare the squid. Use a thin knife to scrape out any loose membrane from the inside of the squid tube, being careful not to cut through the sides. Pat squid dry with kitchen paper and place in a large bowl.
In a small bowl mix the chilli jam, garlic, lime juice and some seasoning. Add half the chilli mix to the squid along with the oil; toss to coat. Stir the coriander into reserved chilli mix.
Barbecue the lemon wedges for 2min on each side until charred. Squeeze the juice into a bowl and mix with the mayonnaise, garlic, and some seasoning.
Barbecue the squid, or cook in a large griddle pan, over very high heat for 2min per side, until lightly charred. Brush with the remaining chilli jam, cook for 30sec more then remove to a plate and serve with the lemon aioli.