This page explains both how to successfully carry out the harassing passengers activity, and the effect on the BGS (Background Simulation). Use the tags above to read about related items, together with similar/related functions in-game.
Passenger missions are in a separate section of the station menu. If you see the Horizons icon, they involve (or may involve a detour to) a planetary landing. A crown icon indicates a VIP.
Harassing passengers involves accepting passenger missions for the faction whose Influence you wish to lower, and then bashing said passenger off of the mail-slot and side of the station until they demand to be returned. Bonus points for ejection. Make sure you don’t end up Hostile in a system where you need to dock & continue performing BGS.
Functional States: All but War
Target/Source Info: Take missions from the faction you want to undermine.
Exceptions: Does not affect INF in War state.
Effect on Player: Loss of REP with mission-giving faction