The choice they want is 'B'. But that's a terrible way to describe what happens.
The volume of the balloon never needs to change.
When the burner turned on, it creates some fiery hot air right above the flame. The fiery hot air quickly rises to the top of the balloon, forcing some not-so-hot air out at the bottom.
The fiery hot air is less dense than the air that got forced out, so now, the average density of all the air in the balloon has decreased.
Since its volume hasn't changed but its average density has decreased, the buoyant force on it (it's floating in air) has increased. The balloon either descends slower than before, or else rises faster than before.