Place the oven rack in the center of the oven, preheat the oven to 375 degrees. Spray a baking sheet with nonstick spray.
Press the spinach between layers of paper towels to remove any excess moisture. Place the cheese in a medium bowl and mash with a fork. Add the spinach, scallions, egg white, dill and pepper together until combined.
Set the stack of phyllo sheets to one side, keep covered with a sheet of wax paper and a damp towel on top as you work.
Lay 1 phyllo sheet lengthwise in front of you and brush the sheet lightly with oil. Top with another sheet and brush lightly with oil. Cut crosswise into 6 oven strips. Place a scant tablespoon of spinach mixture at the end of each strip. Fold one corner up over the filling, then continue folding in a flag fashion to form a triangle. Place on the baking sheet and repeat with the remaining filling and phyllo sheets to make 24 triangles. Brush the tops of the triangles lightly with any remaining oil.
Bake until golden brown, about 25 minutes. Cool for 5 minutes and serve hot or warm.