The idiom bone to pick means to have something you want to discuss with another person or organization. The discussion topic is usually something bad, like hurt feelings or a wrongdoing.
All sources agree that it comes from a dog gnawing a bone after all the meat is gone. The phrase is used for a topic or discussion that one person does not want to let go of, even if all the ‘meaty’ discussion about the topic has already happened.
The entire idiom is usually in the construction (subject) have a bone to pick with (direct object).
A person may have a few bones to pick. Another common phrase is I/I’ve got a bone to pick, but this is considered slang and should be avoided in formal works.
In her statement, Quevado said Polley told Koons she “had a bone to pick with him. [Silver City Sun News]
However the presenter has a bone to pick with some people, who claimed that 1000 Heartbeats was somehow a step back for him. [Daily Record Scotland]
Missouri citizens from across the state have contacted Shaul, many applauding, but other having a bone to pick with the sponsor. [The Missouri Times]
The kitchen has gone beyond too hot and chefs with a bone to pick will fight it out one-on-one in the latest version of the Bravo “Top Chef” series, “Top Chef Duels.” [The New York Daily News]
Hillary Clinton, for example, has gained some recent notoriety for having bones to pick with several people within her own party. [Guardian Voice Live]