Reparations

Not a good quest to have to complete. It is probably better to load an earlier game.

Walkthrough
You get this quest after breaking the rules of the Thieves' Guild, either by killing another member of the guild or stealing from them and getting caught. It is advisable to wait for the members to cool off (about 48 hours or so) before trying to get back into the guild.

Speak with Vex
Speak with Vex about getting back in.

Bring gold to Vex
Pay your fine and get on with your life as a reinstated member.

Wiedergutmachung