Very good question! To me, three central ideas that you could refer to in your middle paragraphs would be: the setting and context, the personal background of Trevor and finally how Trevor mobilises the gang and their purpose in destroying the house.
Greene was writing this story about, among other things, the post-war malaise that resulted from children growing up in a world where the only reality they had ever known was war and its aftermath. The effect on this new generation was widely debated, as many thought war had destroyed the moral basis of society and had resulted in a collapse of hope, especially amongst the youth. Note how this setting is conveyed through the use of description and imagery by the focus on a drab part of the city still recovering from the impact of war. For example, "The gang met every morning in an impromptu car-park, the site of the last bomb of the first blitz." Through such description, Greene establishes a seedy setting which adds to the pessimistic mood of the story.
It is important to focus on what we are told about T.'s background - his father's former career as an architect and his mother's feeling of social superiority, no doubt resulting in lots of pent up anger and frustration in T. himself - and also giving us clear ideas as to the attractions of destroying a house like Old Misery's - which was built by Wren and had been standing for 200 years old. In T.'s mind, destruction can be seen as "a form of creation", after all. You would do well to examine how T's eyes are described as well.
Lastly the gang reject all other worldly reasons for destroying Old Misery's house - they do not do it to gain his money, for vengeance or hatred (in fact they do everything they can to look after Old Misery), rather they do it as a nihilistic statement which reflects their view of the world and their complete rejection of what the world finds meaningful. Consider how the boys burn his money as "something special".
Hope this gives you a few ideas! Good luck.