It comes after the Duke of York, 61, was accused by a judge of “actively evading” efforts to serve the lawsuit to him formally, with Ms Giuffre’s team saying he has been thwarting the attempts.
One of the photos released by law firm Boies Schiller Flexner LLP shows an envelope, addressed to the Royal Lodge in Windsor, being put in a postbox.
It is purported to have been sent by an employee on 9 September and is one of five alleged attempts by Ms Giuffre, 38, to serve papers to which Prince Andrew’s legal team must respond within 21 days.
The UK’s High Court said on Thursday it would arrange for him to be served with the papers if the parties did not work out their own arrangement.
But the jurisdiction does not cover Scotland, prompting speculation that the prince could change his address to Balmoral.
Amid the quarrel over whether the papers have been properly served, Ms Giuffre’s lawyers said: “Service is not intended to be a game of hide and seek behind palace walls.”
Ms Giuffre has accused Prince Andrew of battery and intentional infliction of emotional distress over the alleged incidents when she was 17, which he vehemently denies.
She has spoken publicly about the events – which she says happened around the time financier and convicted sex offender Jeffrey Epstein was abusing her – on several occasions.
New York district judge Lewis Kaplan has said a plan to deliver the papers to Andrew’s lawyer in Los Angeles was “reasonably calculated to bring the papers served to the defendant’s attention”, whether he “authorised” the lawyer to accept it or not.
But Ms Giuffre’s lawyers argue they were sufficiently served in England when a copy of the lawsuit was left with a police officer outside his home in Windsor.
The civil lawsuit seeks unspecified damages. The duke’s lawyer, Andrew Brettler, told a court hearing on Monday that the case is “baseless, nonviable and potentially unlawful.”