Ability to drop missions
... You can go to the contact that gave it to you (or call them) and drop it.
But you can only do one drop every 3 days.
-Rachel-
Yeah, we already have this.
As mentioned, the game already has this.

Iscariot's Guide to the Tri-Form Warshade, version 2.1
I'm sorry that math > your paranoid delusions, but them's the breaks -- Nethergoat
P.E.R.C. Rep for Liberty server
So here is something I think all of us at one point or another wish we could do. Maybe we started leveling in sewers, or maybe just had a few unfortunate groups that never selected your missions as you were leveling, and all of a sudden when you check your mission log, they are all several levels below you!
Wouldn't it be nice to be able to give your contact the bird and say - sorry, that mission is beneath me now? As it stands now with a mission cap of 3, you have to clear out the lower level missions before you can accept any new ones, and if you plan on using all of your mission slots for new content, that means clearing out ALL of your old missions.
Can we get an option either via right clicking, or adding a button on the task to drop the current mission? Please!?