how do you remove some brass pipe mistakenly screwed into a plumbing fixture (wrong piece) which broke off at?

the edge? There's nothing to grab on to, and I don't want to harm the threads on the original fixture. The brass is kind of soft, just not soft enough to pull out with needle nose pliars, I sprayed WD-40 and tried to rotate it, but I can't. It's an expensive piece of bathtub faucet and I don't know what to do?