The important detail about the conflict that Montresor excludes from his version of the story is the following one:
B. Montresor does not reveal exactly what Fortunato did to cause the offense.
Explanation:
The reader learns Montresor hates Fortunato for "the thousand injuries" and also "insult". However, the narrator does not reveal exactly what Fortunato did that was so insulting and caused the narrator to seek revenge. The reader learns Fortunato is an arrogant man (that is how the narrator describes him throughout the short story), but the narrator is quite vague in terms of offering the slightest clue of what it was that triggered his hatred.