The British monarch made the remarks on Thursday during a conversation at the opening of the Welsh Parliament in Cardiff.
The Queen was chatting with the Duchess of Cornwall and Elin Jones, the parliament's presiding officer, when her remarks were captured on video.
At one point, the Queen appears to be talking about the COP26 climate conference in Glasgow, saying: "I've been hearing all about COP ... I still don't know who's coming."
In a separate clip, the Queen appears to say it is "irritating" when "they talk, but they don't do." Parts of the two clips were inaudible.
In her reply, Jones appears to reference Prince William's remarks from earlier Thursday, saying she had been watching him "on television this morning saying there's no point going into space, we need to save the earth," the PA Media news agency reported.
The Duke of Cambridge spoke about the ongoing rush for space travel in an interview with the BBC's Newscast podcast, which aired on Thursday.
"We need some of the world's greatest brains and minds fixed on trying to repair this planet, not trying to find the next place to go and live," he said.
His comments aired the day after "Star Trek" actor William Shatner, 90, made history by becoming the oldest person to go to space aboard a New Shepard spacecraft, developed by Jeff Bezos' Blue Origin.