Honour is used here as a synonym for respect. Sebastian has never tended to respect much of anything, but at least he understood and respected the very reasonable assumption that she would not wish to have contact with him after she married someone else.
Drawing a line beneath a sub-total is a metaphor for treating a part of one's past life as closed, something never to be discussed or even mentioned. William Trevor was writing in those ancient days when people did their accounts with pen and ink.
Student or Learner