If you are referring to the, what looks to be a remaining old skeleton on the right side of the Rhodactis mushroom pictured.
I could be wrong but it looks like a bryozoan to me, pretty rare to see. Last time I saw this was about 15 years ago on a live rock shipment, a book ( i forget the name of the publication) referred to it as birds beak coral, even though it has a hard stony skeleton its not really actually a true coral, just going off the top of my head though, so again could be wrong. Very little out there about this family of animals.