How Do I Remove Embedded Metal From My C5 Collet?

I would also investigate why it is happening. Is the collet not sized properly (perhaps the bar-stock is slightly undersize/oversize)? 

In order for the metal to embed in to the collet the collet must be softer. Is the collet hardened? Or, is it a soft collet that was used to make a custom shape such as an "emergency collet"? Could this be trash build up from the scale on the outside of the bar stock? If this is the case then a small round wire brush that will fit in the collet should do the trick.

I'm assuming that this is a smooth bore collet. I have found that this is often the result of the bar (or piece part) spinning in the collet. If the built up metal covers a small area, you can try to remove it with a Dremel tool or a carbide burr. However, I have found that this is usually just a temporary fix. Once the collet has built up metal the problem will almost always return.

One other thing, if a large area of the collet is damaged, there is not much you can do. Trying to remove a large built up area will cause concentricity problems.