When traveling the main roads why are there always a couple of Alik'r questioning a Redguard woman?? They get on my nerves. I always kill em.

You don't get a bounty doing that?

I enjoy being on the roads, lots of interesting stuff happens.

it has to do with a quest that you can start in Whiterun.

I remember the quest. I completed it very early in the game.

Of course, but you still get this random encounter long after you complete the quest.

Actually yes, but if you kill the Redgard woman the bounty is lifted because she's the last witness.