Place the steaks in a sided dish. Pour in the teriyaki sauce; cover and marinate in the fridge overnight, turning occasionally. Place the squash, ginger and garlic in a pot and cover with lightly salted cold water. Boil the squash until tender. Meanwhile, heat an indoor or outdoor grill to medium-high. Remove the steaks from the marinade; discard the marinade. Lightly oil the grill. Grill the steaks to the desired doneness, allowing 2 to 3 minutes per side for rare, and 3 to 4 minutes for medium-rare to medium. When the squash is tender, drain well and thoroughly mash. Mix in the butter, salt and pepper. Divide the mashed squash among four plates, set on the steaks and serve.
Note: Cleaned (the seeds removed and cut) banana squash is available in the produce department.