ExcitedMum2B:I have the backpack one and it removes, but I found it's easier to just keep it in there since I have to carry all that stuff back and forth from work anyway. Make sure you get the bra too, I wish I had gotten it weeks before I did.
If you don't want to buy the bra, I made my own. Just use an old tight sports bra and cut a slit in the fabric where the nipple is to insert the pieces through.