Before previewing the new Catheter Cowboy ad, Oliver devoted nearly his entire programme on Sunday night to discussing Trump's often fallacious criticisms of the deal - in particular his claim that Iran can simply start developing nuclear weapons again when parts of the deal expire in 10 years.
As the Washington Post's Fact Checker has written, Trump has ignored a clause in the deal that permanently bars Iran from acquiring nuclear weapons. In Oliver's PSA, set to air in Washington during Hannity's programme this week, the cowboy delivers a somewhat simpler message to the president.
The spot begins as a shot-for-shot re-creation of a 2015 ad opposing the Iran deal, in which an American family sits down at a dinner table and abruptly disappears in a nuclear explosion.
Instead of a nuclear fireball, this time the Catheter Cowboy intrudes on the family, wearing the same plaid shirt and leather vest from his Medicare days.
"Hey there, Donald, sorry to interrupt your supper," he says, addressing the camera while the family stares at his back. "I'm here to tell you the Iran deal may not be perfect, but it helps restrict Iran's ability to start making a bomb for at least 10 years.
"If you blow up the deal, that turns into zero years. And if I've learned one thing from all these years of cowboying and cathing, it's that 0 is way less than 10."
He holds up two posters, a '0' and a '10,' to reinforce the message. He then holds up a third card displaying the face of Trump's new national security adviser, John Bolton, who founded the nonprofit that made the original dinner-table ad in 2015.
"Also, do you really want to listen to a guy with a mustache like this?" the cowboy says. "Don't do it, Donald. Don't do it. Hey, does anyone smell gas?"
"Oh my God, the stove!" says the wife at the table, at which point the house explodes in a fireball, as in the original.
Oliver despaired that the ad may not do much good. He noted that Trump has surrounded himself with opponents of the Iranian nuclear deal - including Hannity, who once said it would lead to a "modern-day Holocaust," and who The Post reported is a close confidant of the president, besides hosting one of his favourite shows.
But, Oliver told his viewers, sending a cowboy to speak to Trump between segments of Hannity was as close to influencing the president as he could come.
"It will presumably confuse a lot of people," the host said. "I'm not saying it's going to change anything, but at least we will know that we tried."