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 weight of the children will change due to the difference in gravity. However, their masses remain the same regardless of the location. Since the seesaw balances based on mass and the position of the children, they will still balance on the Moon if their masses (and lever arms) are the same as they were on Earth.