The symbol is a circle of four swords laid out in a cross pattern inside a circle, since they're basket-hilted rapiers or sabres they stylized look like lower-case p's. I'm actually not sure if the emblem is supposed to be right-angled cross or a saltie-type cross. (it seems to vary depending on depiction) I don't really see anything even resembling a swastika this depiction (apart from the fact that a Swastika too is a kind of cross) if anything it looks more like the keys of St. Peter or something.
The Good Mark represents the four swords laid down by four pirate captains defeated by one of the early Phantoms, who ended up founding the jungle patrol.