XenonS: You must return to the base computer of your 1st built base and activate the mission, then interact with the BC when you see the red symbol over it.
If you are deeper in the game ignore this mission, it doesn't give you anything important, most often it gives you C-Class ship upgrades that you can easily find at the vendors on space stations. Not worth to lose your time and there is no way to delete it from your log, at some point it disappears on its own.