In a large freezer bag combine 1 cup water, 3 tablespoons fresh lime juice, 2 tablespoons soy sauce, 1/4 cup sweet chili sauce, 1/2 tablespoon Worcestershire sauce, 2 minced garlic cloves, black pepper to taste, 1/2 teaspoon ground cumin, and the chicken cutlets. Seal the bag and massage to coat the chicken completely.
Refrigerate the sealed bag for up to 24 hours to marinate, ideally at least 30 minutes.
While chicken marinates, make the pico: in a small bowl combine 3 diced roma tomatoes, 1/4 cup finely diced yellow onion, 1/4 cup chopped cilantro, and the juice of 1 lime; season with salt and pepper to taste and stir to combine.
Preheat the grill to medium heat (or heat a grill pan over medium). Remove chicken from the marinade and discard the marinade.
Grill the chicken cutlets 2–3 minutes per side, until cooked through. When flipping to the second side, sprinkle each cutlet with shredded cheddar so it melts; cover the grill or loosely tent with foil to help the cheese melt and finish cooking.
Remove the chicken from the grill. Top each cutlet with pico de gallo and tortilla strips, then serve immediately.