you can remove the antenna since it's worthless anyway, it's only for AM/FM reception, w/out the antenna your range is just not that huge on AM/FM that's all. it doesn't affect the rest of the base where GPS is etc.
if you're really picky you can get a nylon screw that matches the threads and shorten it so it plugs the hole beautifully.
other options of course Cravenspeed shorty (super nice) antennas but not in production yet, the more requests they get the faster they'll make them for the GC.
here's an example of the Cravenspeed
on a mini cooper