Wrap the tofu in paper towels and set a heavy object (like a cast iron skillet) on top. Let it press for about 30 minutes to remove excess water.
Slice the pressed tofu into four equal slabs and coat each side with the marinade. Let it marinate for at least 15 minutes to soak up the flavors.
Use oil to brush the grates, which helps prevent sticking. Add the tofu slabs to the grill and cook for 3-4 minutes on each side until charred and easily releasing from the grates.
Once cooked, take them off the grill and serve right away. If desired, drizzle with a little reserved marinade and sprinkle with green onions, if using.