To make the pico de gallo, stir the chopped tomatoes, red onion, jalapeno, cilantro together in a bowl with the juice of 1 lime and a pinch of salt and pepper.
Slice the remaining 2 limes into thin wedges for serving.
Heat grill to high.
Place closed oysters on the grill and cook covered, 5-7 minutes or until opened (smaller oysters will open in ~5 minutes, larger ones might take a few more minutes).
Remove to a platter and let cool slightly.
If any of the oysters remain closed, throw them out – they are not safe to eat.
Preheat the broiler.
Using a dull knife, pry the shells completely open and discard the top shell.
Top each shell with a pinch of shredded jack and place on an oven-safe dish/baking pan (covering the bottom with something like dry beans, uncooked rice, or salt will keep the oysters from sliding around or tipping over).
Broil for ~1 minute, just to melt the cheese.
Top with a spoonful of pico and serve immediately, with extra lime wedges.