(CNN) The grieving parents of a British teenager say they are "extremely angry" and feel they have been "taken advantage of" after a highly choreographed White House encounter with US President Donald Trump -- where he presented them with an unexpected offer to meet the woman involved in the crash that killed their son.

The family says that Trump surprised them with the "bombshell" news that Anne Sacoolas, the wife of a US diplomat stationed in the UK , was in an adjoining room. Photographers were waiting in the wings, said a family spokesman, who described the encounter as an ambush.

UK police said Sacoolas claimed diplomatic immunity in the aftermath of the crash that killed Harry Dunn, 19, and left the country three weeks later. Through her attorney, she apologized for a "tragic mistake." Police say their investigation is not yet complete.

Dunn's parents are in the US this week to make the case that Sacoolas should be returned to Britain to face justice, and met with Trump at the White House on Tuesday.

"President Trump came off as a very warm, engaging guy, he makes you feel really special," Radd Seiger, the family's spokesperson, told CNN. "But once the pleasantries were over, and we sat down, he said: 'Let's cut to the chase. You want to meet Mrs. Sacoolas. I can make that happen."

"She was next door. It was a shock," he added.

Charlotte Charles, Dunn's mother, told British TV station Sky News that the family declined the offer to see Sacoolas at the White House, because the family wants a meeting on "their terms" and "on UK soil."

Trump said Wednesday that he had met with the family at the request of British Prime Minister Boris Johnson. He described the meeting as "beautiful in a certain way" and that he "expressed condolences on behalf of our country" during the meeting.

"I offered to bring the person in question in, and they weren't ready for it," Trump said during a Oval Office meeting Wednesday.

Seiger responded to Trump's comments with a fiery statement that described the meeting as "a stunt to make President Trump look good" and suggesting that the surprise offer to meet Dunn was a false choice.

"It is not up to them. Right from the outset, the family has said that Anne Sacoolas has to come back to the UK to face the music. There has never been any change in their position," the statement read.

"We are extremely angry, this family feels it has been taken advantage of, that they have become a pawn in a wider political game," it also said.

Dunn died in on August 27 outside a base controlled by the US Air Force in central England after his motorbike was struck by a car driven on the wrong side of the road by Sacoolas.

She originally cooperated in the case, British police said, but later left the country, protected by diplomatic immunity, despite assuring them she would remain in the UK.

In a statement, police say their investigation is still underway. "We are working very closely with the Crown Prosecution Service with whom we visited the collision site earlier today. It's our expectation that we will be able submit a case file very shortly to the CPS."

Harry Dunn, 19, was killed in a road crash in August.

Earlier on Tuesday, her attorney, Amy Jeffress, released a statement expressing remorse for the tragedy. "Anne was driving on the wrong side of the road and is terribly, terribly sorry for that tragic mistake. Neither she nor Harry Dunn's family will ever be the same because of it. She wants to meet with the family to apologize and take responsibility."

Jeffress says her client met with police twice -- on the day of the incident and at her home the following day. After providing a statement at the scene and meeting officers the next day, she had no further contact with the police, Jeffress said. "She and her family left the United Kingdom approximately three weeks after the accident, after they and the US authorities determined that it would be difficult for the couple and their children to remain in the small Croughton community under these tragic circumstances," the lawyer said.

"Our understanding is that the British authorities were informed and aware of their departure before they returned to the United States," Jeffress added.

Seiger, the family spokesman, said the meeting with Trump appeared to have been orchestrated. After the family declined the meeting with Sacoolas, Seiger said he noticed a bank of photographers, who seemed to have been positioned to capture the dramatic moment. "Clearly they were looking to get a photo of the President introducing Mrs Sacoolas to Harry's parents," Seiger said.

In a separate interview with the BBC, Seiger said the encounter felt like a setup. "I think the family feel a little bit ambushed to say the least," he added.

Seiger told CNN the family felt Trump had convened the meeting for his personal gain. "We feel a little numb. There wasn't any real progress, apart from right at the end, the President saying he would look at it from another angle," Seiger said. "Reflecting on it this morning, I think Charlotte and Tim realize that the President was only doing it for himself."

The family says that Trump did not promise to return Sacoolas to the UK.

Under the 1961 Vienna Convention, diplomats and their family members are typically immune from prosecution in their host country. The US State Department told CNN Saturday that diplomatic immunity is "rarely waived."

However, the UK Foreign Secretary Dominic Raab said in a letter written to Dunn's family that Sacoolas' diplomatic immunity "is no longer pertinent."

"We have pressed strongly for a waiver of immunity, so that justice can be done... Whilst the US government has steadfastly declined to give that waiver, that is not the end of the matter," Raab said in the letter seen by CNN.

"The UK government's position is that immunity, and therefore any question of waiver, is no longer relevant in Mrs. Sacoolas' case, because she has returned home," he wrote.