Plug broke in 12v socket

My GPS adapter's plug broke in the socket when I pulled it out, and I'm not sure if a piece of still stuck inside the socket. I can't really tell since I don't remember what the socket looked like on the inside before this happened.

I've attached a pic of what it looks like. That piece on the bottom is some sort of white plastic. Can anyone compare this with theirs and let me know if I should try to pull that piece out? The car is a 2007 Versa Sedan S.