I don't know if I necessarily agree that T. is "mentally disturbed" as you put it in your question. However, semantics apart, we are given a real indication about T., or the "new recruit", in the second paragraph of the story which gives a real insight into the way he thinks and also gives us a real clue as to his motivation for the destruction:
...the fact that his father, a former architect and present clerk, had "come down in the world" and that his mother considered herself better than the neighbors.
Thus we can see that T. has suffered both in terms of being raised in an atmosphere of conflict and resentment but also in terms of growing up in a post-war reality that has been the only world he has ever known - a time of the moral destruction of society, the collapse of hope and the onset of cynicism and despair. In this environment, therefore, we can understand why T. takes such an obsessive, focussed interest in the destruction of the house, for as the story says, "and destruction after all is a form of creation."
I wouldn't say so much as mentally disturbed as I would clever. Btw his parents are not divorced it never says they are, Greene just describes them individually.
The fact that his father is a former architect says that T knows a thing or two about buildings. Surrounding Old Misery's house is nothing but bombed out places. Look at the ending when the man who is driving off with a rope (little does he know) tied around his bumper finished the boys job and pulls the outside of the walls down. Mr. Thomas is sad and the man laughs I would question that more than T. Where is this man's sense of humor coming from? Is it the fact that now Mr. Thomas' house matches the rest of them, demolished?
Two things, the World War II intense bombing period known as "the Blitz" and his parents divorce. Both have a powerful effect on the human psyche and they both did so with Trevor, causing the line between rational and irrational to blur.