The egg cases are spiral shaped and won't be killed by freshwater or iodine dips. You have to pick them off with tweezers.

Those zoas will do fine in an unbuffered fw dip. I take a cup of RO water and add a little Seachem Reef Dip and vigorously shake the zoa frag or rock around to dislodge any and all pests and critters. Let it sit for a minute or two and shake again. You can also use Lugol's (one drop will do in a gallon) or Revive coral cleaner. I have good results with all. Before placing it back in tank, dip in tank water or fresh untreated RO.