Preheat a grill pan or a grill to medium-high. Soak the bamboo skewers in water, particularly if you're using an outdoor grill, so they don't flame up.
Place the beef strips in a medium-large casserole dish and pour 1 cup of the teriyaki sauce, the crushed garlic and chili oil over them. Toss to combine and let the beef marinate in the refrigerator while you make the dipping sauce.
In a medium-size saucepot, add the remaining 1/4 cup of teriyaki sauce, apple juice, and the ginger. Once it reaches a boil, turn off the heat and let it sit for 2-3 minutes to incorporate the ginger flavor. Remove the ginger and reserve the liquid.
In a medium-size mixing bowl, whisk together the peanut butter, lime zest and the hot teriyaki/apple juice mixture until it resembles a dipping sauce consistency. Place the sauce in a serving bowl, and set it aside while you grill up the satays.
Remove the beef strips from the refrigerator and skewer the strips of meat by weaving the sticks in and out as if you where treading straight up the meat. Grill the satays for about 1-2 minutes on each side for medium-rare, then give them a quick squeeze of fresh lime juice for a finish. Garnish the dipping sauce and meat with the scallions and toasted sesame seeds.