How to remove this eccentric bottom bracket?
Those are self extracting crank bolts. 

Sram / TruVativ use them. They work like a charm. 

The BB cups require a special wrench. The BB should be a Sram / TruVativ GXP. 

These require a special wrench that will be referenced as having 16 notches, as there are 16 depressions in your BB. 

You can find cheap ones or expensive ones. Up to you. 

Remove the BB cups, clean everything really well, grease generously and put a new GXP. 

They are well priced, and in my experience they are reliable and efficient. Also you couldn't get any easier to adjust. Good luck!