The correct response is:
Yes, they would still be balanced because their masses would not change.
On the Moon, the gravitational force is weaker than on Earth, which means that the weights of the children would decrease. However, their masses would remain the same. The seesaw balances based on the ratio of mass and gravitational force (weight), so as long as the ratio of their masses remains the same, they will still be balanced even though their weights are different.