Hero Cat -- Family Will NOT Sue Dog Owners

12:10 PM PT -- Tara's owners were just on TMZ Live ... and explained why they're not suing their neighbors. They also talked about Jeremy's recovery from the attack.

You gotta see the kid ... he's cute as hell.

The owners of the dog that mauled the boy who was miraculously saved by his cat have just gotten away with metaphorical murder ... because they'll have to pay next to nothing and they've dodged a lawsuit.

Erica and Roger Triantafilo tell TMZ ... their insurance will cover almost the entire medical bill, so the only thing they want from the dog owners is the deductible -- $155!!!

The attack -- now seen 'round the world -- could have turned into a wrongful death case were it not for the pet cat, Tara, which chased the dog away. As it stands, the injuries little Jeremy suffered were serious. And Erica tells us ... she too was bit on the leg as she tried to save her son.

Erica says her family is not looking to punish their neighbors. In fact, she says they're still friends.

As for the dog ... it will be destroyed.

Bullet dodged.