This egg was only available in Egg Cave's Cash Shop Park for June 2012.
If you attempt to pick up a Gadfly egg, your hands will go straight through it, as if you were trying to catch the wind! The only material that can physically hold a Gadfly egg is platinum metal. It's not uncommon to see Ark residents transporting their Gadfly egg on platinum trays and holding the egg with platinum gloves.
Gadflies are like ghosts, not because they can't be seen, but because they cannot be touched by any material thing (your hands will go straight through them!). Unlike the Gadfly egg stage, platinum metal makes no difference (it also flies straight through).
No hugs for your Gadfly!