Which one.......the extractor or the ejector? They are different parts. The extractor is the long part on the right side of the slide with the "hook" that grabs the case rim. The ejector is the "pointing finger" looking part that is on the top rear of the frame on the left, it is what "ejects" the round out as the slide reciprocates.
Either way, I'd just spray some gun scrubber or SimpleGreen around them rather than removing them.
The manual for the P99 has diagrams that show how to remove the striker assembly. Taking it off is easier than putting it back on, but neither is a terrible undertaking.
If you don't have the manual itself, it is also available online here; Walther Online Manuals