The mission also does not clear for me. I have done it 6 times, each time answering correctly and being told to depart since the mission is over. Admiral Quinn gave me new missions the first time I tried to turn it in, but he isn't doing anything any more.
I have found several missions during my Commander Rank that would not complete.
Every case was where I had chosen "Not Now" to leave after the mission was completed.
I would then would have the Depart System objective listed but leaving the system would not complete it.
To fix this I had to team with someone to reset the spawns in the mission (due to going back into the system was always empty from me having cleared it already) and choosing the option to depart the system.
Was fine on first character, but running into this problem with my second. First attempt was in an open instance team. After completion, returning to sector space only showed the mission still being open.
Tried everything possible to resolve: changed team settings to closed group, dropped the mission (the system patrol, not the sector patrol), logged out. Only thing I haven't tried yet is close the game and then restart it, but I doubt that will make any more difference than logging out would...
Also, tried leaving the group before beaming down, but this only lead to either a message giving me a countdown until leaving the map (like in PvP once it finishes), or, once on the planet, the option to depart the system.
In none of these cases, completion gets credited, meaning this mission is unresolvable to my second character... Also already put this in a GM request/bug report.