How can I remove this concrete wall anchor?
These don't come out easily, sometimes they can be pushed back into the wall and dissappear, this is often the case if the person installing it was thinking ahead and drilled the hole deeper than needed as an end-of-life plan. 

Else you need to drive the shaft back in a bit to release the wedge and then pull on the sleeve part, locking pliers are useful here.

If it won't budge the easiest fix is to chop it off using an angle-grinder with a cut-off wheel and then drive it back into the hole a bit and plaster over it.