Last Updated Oct 16, 2019 10:43 AM EDT
The, who was killed in a traffic accident involving American Anne Sacoolas, tells "CBS This Morning" they rejected President Trump's surprise offer to meet with Sacoolas during a White House meeting on Tuesday.
After offering them his condolences, "it didn't take long for [Mr. Trump] to then drop into the conversation that Anne Sacoolas was in the building," mother Charlotte Charles said in her first U.S. TV interview since the meeting.
Dunn's father, Tim, said when he first heard the offer to meet with Sacoolas, it took his breath away.
"He did ask two or three times," Tim said, adding, "It was a bit pressure, but we stuck to our guns."
Charles said it was the "wrong setting."
"We've said all along that you know we are willing to meet her. We are still willing to meet her. But it needs to be on U.K. soil, you know, and with therapists and mediators," Charles said. "And that's not just for us. That's for her as well."
Sacoolas' lawyer told CBS News that Sacoolas was invited to the White House, but wasn't aware of the circumstances of the meeting.
"To be thrown into a room together with no prior warning, that's not good for her mental health, it's certainly not good for ours… You know, none of us know how we were going to react to have that sprung on us," Charles said.
"I think the family feels a little ambushed, to say the least," the parents' lawyer, Radd Seiger, told the BBC.
Charles and Dunn said Mr. Trump did not seem responsive to their request to have Sacoolas return to the U.K. to face justice. Sacoolas, who is reportedly married to a U.S. intelligence official, left the U.K. after the crash claiming diplomatic immunity. Police said Sacoolas struck Dunn in August after she was driving on the wrong side of the road near a U.S. military base.
Charles said she asked Mr. Trump who allowed Sacoolas to return to the U.S., but did not get an answer to the question.
"At the end of the meeting, we all shook hands, and I ended up at the back of our little family queue and President Trump actually grabbed hold of my hand. So I squeezed it tight, and I just said to him, 'Please, you know, just do the right thing. You know, if you had a son, you'd be doing the same. You've said that.' And he said, again, he said, 'I absolutely would.' And he said that he would maybe now look at the possibility of looking at it from a different angle."
While unclear what that meant exactly, Charles said it gave her "just a little bit of hope that he might actually carry that through."
Getting Sacoolas back to the U.K. is still the parents' "main aim."
"She's held her hands up again in a statement this week saying that it was entirely her fault, she made a mistake. So stand up to your mistakes. Take ownership of them," Charles said.