Gum is an item featured in Freddi Fish 4: The Case of the Hogfish Rustlers of Briny Gulch. It can be purchased from Gill Barker for two purple sea urchins. If the gum is being chewed by the Hogfish, it is one of the evidence that show if Gill Barker is Mr. Big and the mastermind behind the rustling.
Freddi and Luther have their opinions on what the gum tastes like. The gum can also be offered to other fish and they all give their reasons as to why they don't want it.
In the path of the game without the Shark, it's still possible to purchase the Gum, but not required for beating the game. If Freddi and Luther do purchase it, it'll remain in their inventory for the rest of the game, since it cannot be used for anything else.