Preheat grill over medium-high heat. Lightly brush turkey burgers, pineapple, and scallions with oil and season generously with Kosher salt. Grill burgers on each side until cooked through, about 5 minutes per side. During the last 2 minutes of grilling, brush half of the teriyaki sauce on the burgers. Grill pineapple, flipping once, about 3 to 4 minutes per side. Grill scallions, turning as needed, until charred in spots, about 4 to 5 minutes total.
Finely chop charred scallions and in a small mixing bowl, combine with mayonnaise and minced garlic. Season with Kosher salt.
Place a turkey burger on each bun and brush with more teriyaki sauce. Top with mashed avocado, a grilled pineapple slice, and a good slathering of charred scallion aioli. Devour immediately.