Does anyone know how to remove the base attachment for the front license plate from the car?

 

hooooooooooooooooooles! Unless you want to do body work or put plugs in you will have 4 very unsightly (imho) holes in your front clip.

to your original question. You will probably have to take the whole clip off to remove the hardware from the inside.

 

Just pull once the screws are out. They are held in by rubber expanding anchors. No need to remove the bumper cover.