(You may have to use a thinner item, such as a small screwdriver, or a thicker paperclip; depends on the brand, again. For a Bic, a fork should work pretty well.) This forces the safety out from the prongs which hold it in -- although it should be mentioned, for the sake of safety, that sometimes it pops out fully and can hit you in the eye.

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From there you can simply use needle-nose pliers or fingers as above to remove it fully. This often saves you from having to re-adjust the prongs, which can often nick your thumb, even after they've been flattened. If the prongs actually came undone, just push them back in with a hard flat object, such as the butt end of the screwdriver. You can even just press them against the edge of the table.