If the store named "(thing) Joe's" builds its entire business on "we sell Trader Joe's products", there is a very reasonable case that they're confusing (possibly deliberately confusing) the public about whether they are or are not an actual Trader Joe's. Which... brings trademark law into play.
So, like I said. Maybe it's time for you to go back to law school.
It is not plausible that "Pirate Joe's" is confusing. You can't simply discard "(thing)" and focus on "Joe's", trademarks are taken with their entire context.
So, like I said. Maybe it's time for you to go back to law school.