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.