Puffers Can Be A Nuisance But It's Part Of Fishing!
On days that desirable species can't be caught most anglers in Hawaii grumble about catching Pufferfish (i get teased by my buddies all the time). All the species are poisonous to consume unless you're an expert chef that can cut out the poison glands without rupturing them. So we release them. Some anglers leave them out of the water to kill them because they don't want to hook them again. There's no law to forbid this but most responsible anglers don't kill for selfish reasons.
If you accidentally catch a Pufferfish just release it. Don't kill it. I've caught so many over the years that i can recognize the signs of a Puffer nibbling on the bait. The bell w/bell holder gives them away. This species of Puffer is called a Burrfish. Use pliers to remove the hook as those chompers can take a finger tip off easily.