Baldwin closed down his personal Twitter account earlier this week but has apparently now taken to sending messages from the Alec Baldwin Foundation's page.
Ireland began the conversation by tweeting: "the media and their stories.... THEY LIE ABOUT EVERYTHING."
Her father retweeted the message and added: "Is that true?"
Ireland later added: "The media may not lie about everything but a great amount, yeah", prompting her dad to say: "You have learned well, Grasshopper."
Alec, who recently married his partner Hilaria Thomas, was photographed clashing with a paparazzo last month but later insisted that he is not "decking photographers willy-nilly".
He also described the paparazzi as a "menace", saying: "They're not there to make you look good. The paparazzi are never there to make you look good, never."