The correct option is E The level of geological activity
Callisto's surface is very heavily cratered from the impact of comets and asteroids, and it also reveals no geological activity.
This is mentioned in the line: "Only Callisto reveals no geological activity. In a similar fashion, Callisto's surface is very heavily cratered from the impact of comets and asteroids..."
On the other hand, Lo does not have any craters, and there's a reason given for it as well, that even though Jupiter attracts comets and asteroids, there is more bombardment of the inner moons (Lo and Europa), Lo's geological activity results in volcanic resurfacing and hence, no craters.
It's mentioned here: "...and no craters have been detected on Lo, even though Jupiter's gravity attracts comets and asteroids...increasing the bombardment rate of the inner moons... But because of Lo's high degree of geological activity, its surface undergoes more-or-less continuous volcanic resurfacing."
Between these two moons, we can conclude that it is the level of geological activity (negligible in Callisto and very high in Lo) that determines the amount of cratering on their surfaces and that the difference between their cratering is explained by the difference between their geological activities.
Hence option E is correct.
The rest of the options 'size', 'ice content', 'rate of bombardment', 'influence of Jupiter's other moons' do not affect the cratering of the surface of these moons, as their geological activity eventually does.
Hence options A, B, C and D are incorrect.