Chatting to Sir David Attenborough as they stroll through Buckingham Palace's gardens the Queen says "sounds like President Trump, or President Obama", when the peaceful setting is shattered by the sound of an aircraft.
"Why do they always go round and round when you want to talk?" the Queen says.
In the special, Jolie visits Namibia with her six kids-Maddox (16), Pax (14), Zahara (13), Shiloh (11), Knox (9) and Vivienne (9)-to shed light on forest conservation in Africa and reveals that Queen Elizabeth is an inspiration for her children.
The scene is one of a number of exchanges between the pair - born a few weeks apart - that were recorded for ITV documentary the Queen's Green Planet, to be aired next Monday.
The project, which is spearheaded by Her Majesty, aims to conserve forests in all 53 Commonwealth countries.
Like many a pensioner, the pair are recorded complaining about health and safety and attempts to prevent children playing conkers. Then, after a pause, she adds with a smile: "I won't be here though".
In a separate excerpt from the queen's walk with Attenborough, released by ITV ahead of broadcast, the quiet of the palace garden is broken by the noise of a helicopter hovering overhead.
Another amusing moment occurs when the monarch spots a young sapling tree bent over, saying: "That one we won't look at because it doesn't seem to be doing very well".
"She is very unsolemn, very good at putting people at their ease", he said. "Somebody sat on it, I think at a garden party", she said.
The Queen and Attenborough have known one another since the 1980s, when he worked as a producer on the monarch's Christmas speeches.
"The Queen's Green Planet" will be broadcast in the United Kingdom on ITV at 9 p.m. on April 16.