Tacky Glue is will reactivate if it gets wet... in other words, if you are worried that it might need to be removed that would be a good choice. HOWEVER, if they are planning on hanging it in a bathroom, the starfish would fall off. Silicone glue works quite well on starfish.
The real question here is, is this a piece that will be hung in a moist area?
Would the starfish ever need to be removed?
Is this just a pretty thing to hang?
If it is going in a bathroom, never going to be removed, and just needs to be pretty, use silicone.
If it is going to hang in the living room, might need to be removed, but still is just pretty, use Tacky glue.
If this is going in a museum, must be removed, and is irreplaceable, use mylar / brass rods / thread /or a sink mat.
Remember, we are not magicians. We are framers, and sometimes the mount MUST show. Just don't get carried away when it's just something to make the bathroom pretty.