Answer
The work $W_m$ done by the Earth's gravitational field on the mango is positive work.
The work done by the mango's gravitational field $W_E$ on the Earth is positive work.
The magnitudes and signs of $W_m$ and $W_E$ are the same.
Work Step by Step
The Earth's gravitational field pulls down on the mango as the mango falls down. Since the force is in the same direction as the motion, the work $W_m$ done by the Earth's gravitational field on the mango is positive work.
Similarly, the Earth's motion relative to the mango is toward the mango while the force of the mango's gravitational field on the Earth is toward the mango. Since they are in the same direction, the work done by the mango's gravitational field $W_E$ on the earth is positive work.
The magnitude of the forces are equal, the forces act over the same distance, and the work done is positive work. Therefore the magnitudes and signs of $W_m$ and $W_E$ are the same.
