Well its the popping off the little white caps, I've tried skewers, paper clips, pins, forks all sorts and I can only get it off with it breaking....I have just seen a video showing that you don't have to remove it you can just place it in a juice filled rubber end bit and that soaks it up....is this true?
The entire Key to pulling of a Pesky Cartomizer Mouth Piece is using the Right Tool. You need a tool that has a Hook at the End so you can Tool Under the Mouth Piece and the Pull Up. And the Tool needs to be Stiff Enough to Not Bend.
Many people find that the Wire that makes up the Handle of a Binder Clip works Perfectly. It has a Small Hook on the End of it Already.
As mentioned... Some Cartomizer have a Small Dab of Glue used to keep the Mouth piece in place. This can make it hard to remove the Mouth Piece even with something like a Binder Clip. I have found that Putting about 1/4 Inch of the Cartomizer into near Boiling Water will loosen the Glue enough to make pull out the Mouth Piece Relatively straight forward.
Last thing, there are many choices out there of Blank Cartomizer. So when you start to get low and are ready to Buy more Cartomizers, consider buying Blank Cartomizer with Soft Mouth Pieces and filling them yourself. The mouth piece on the Blank Cartomizer are Much Easier to Remove and Replace.