These are the broken claws of King Nippers.  When Sereness appeared before Giler in the human form was when Gilers pirate ship was in danger surrounded by a group of King Nippers.  After defeating the King Nippers and rescuing Giler, she fell in love with him, a human - an unthinkable deed for a spirit.  Even though she knew that she was only being used by him, she could do nothing else but help them because of her love.