They obviously made a big mistake by sending you a new pen. I looked at mine and it looks the same as yours except there aren't any scragglies hanging off the end. I don't know what could have caused your scragglies. I almost looks like the tip ran across something sharp. I bet a little sandpaper would clean those off and it would work like brand new.
So it is possible to remove end of the pen, not the tip, but the entire cone like shaped part, this includes the small different coloured grey part, and the same coloured, larger, cone part. Beware though, if you use a rough pair of plyers, the coating will come off and the pen will be scratched. You can grab onto the small flat part that the cone has, and untwist the pen. It is quite difficult at start, but gets easier as you go on. The cone part will come off, and you should be able to easily remove the broken part of the pen nib. Putting the new nib and the cone back on is straight forward, just make sure the inside of the pen doesn't twist, otherwise the buttons won't align properly. This is only if your pen nib has been broken, if it's in one piece, you can easily pull it out like the other comments say.
When I bought my SP3 in January, I thought it hadn't come with a Nib (it had come out and settled in the bottom of the packing). I contacted MS and a week later I received 4 replacements in the mail. Way to go MS!