How do I remove the posts that the stop bar tailpiece and tune-o-matic bridge rest on?

Im getting the chrome parts annodized and I need them removed from the guitar to do so.
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Unscrew them?
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Usually if you can find a screw or rock that's long and skinny you can drop it into the stud, then screw the screw ontop of that. The screw should hit the screw/stone after one or two turns and pull up the stud in the body. Go SLOW and don't rush it.
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Hey - I've got kind of a low-intermediate/noob question. I've got an Epiphone Les Paul and was changing the strings this afternoon and the stopbar tailpiece came off, seemingly on its own. I was removing a string that I had restrung badly to do it over again and I noticed that it was only hanging on by one "post". I'm guessing they're not just supposed to come loose like that, or...are they? It's never happened in any of the other 2 or 3 times I've changed strings. Advice?