The Arabic word jihād relates to exertion and striving. This narration singles out an ethical situation in which speaking truth is difficult. Its emphasis is specifically on a word of truth, not a general instruction to seek confrontation.
عِنْدَ is an adverbial word meaning “before” or “in the presence of.” جَائِر denotes injustice; disagreeing with someone does not, by itself, make that person unjust.
Integrity also requires applying fairness in one's own decisions. A person cannot consistently demand justice from others while disregarding it in everyday dealings.