In order not to loose the bits of plastic in the radiator. You should take the inlet hose off and put something in there to catch all the bits (you will lose a bit of radiator fulid) then just push the half that is still in the radiator down into the waiting cup or hand or aluminum foil shaped to fit in the radiator. I made the mistake of pushing the bits down and had to take the whole radiator out. While you are at it get a new hose, mine stared to leak again but I changed the hose and now it is fine.
If you have any more probles this board is the place to go I know it has saved me hundreds of dollars