Difficult to tell from that drawing, but I suspect it's a "fish louse" (Argulus spp.) or "sea louse" (Caligus spp.) similar to those you find on farmed salmon. Not particularly dangerous, though I'm glad you were able to shift yours. Abrupt changes in salinity do the trick, as you've discovered.
When my (freshwater) puffers got sick from some mystery slime disease, I gave them a couple of 10 minute seawater dips, and that cleared it up. Puffers are very tolerant of changes in salinity, but external parasites tend not to be, so this is a good, safe tool to use when keeping them.
Cheers, Neale