Try looping fishing line (or very thin twine or bend a twist tie) around one of the three arms of the poppet. Repeat around the other arms of the poppet, if needed. Then give a gentle tug. If it doesn't work, then using a needle nose pliers to push against the arms while pulling on the fishing line (or twine or twist tie) helps to bend the arms of the poppet enough to allow it to clear the metal rim.