Combine chicken strips and fajita marinade in a large bowl. Let marinate in the refrigerator, 1 hour to overnight. Preheat an outdoor grill for medium-high heat and lightly oil the grate. If you don't have a grill, use a griddle pan. Combine oil, minced garlic, salt, and pepper together in a bowl. Clean heads of romaine lettuce; cut in half from end to end. Brush halved romaine lettuce with oil-garlic mixture. Add sliced peppers and onions to the oil-garlic mixture. Toss to combine. Arrange the romaine cut-side down on the oiled grill. Cook just until grill marks appear, about 2 minutes. Remove and set aside to cool. If you have a grill basket, spread marinated chicken evenly in the basket; otherwise, thread chicken and vegetables on skewers. Grill chicken for 5 minutes. Turn the chicken in the basket, add the vegetables, and grill until an instant-read thermometer inserted in the chicken reaches 165 degrees F (74 degrees C), about 10 minutes more. Slice grilled lettuce and place on serving plates. Divide chicken and vegetables evenly over the grilled romaine lettuce.