Barnes said the agency sold the images, taken on January 20 this year, which show the Meghan and Archie walking with her two dogs, in Horth Hill Regional Park on Vancouver Island.
The case is being brought by Meghan in her own right and by her and the Duke of Sussex, on behalf of Archie.
The Duke and Duchess claim the photographs represent a misuse of Meghan and Archie's private information and are in breach of the Data Protection Act.
They are also pursuing action against the UK arm of the agency.
According to the Daily Mail, Barnes told the court: "In a nutshell, as a claimant lawyer, I would describe what happened to the claimants as being they were 'papped'.
"This was without their acquiescence or consent and it is accepted that it was by an employee of the [US agency], Steve Dennett."
The lawyer continued, saying the pictures were taken during "a private recreational outing on Vancouver Island".
He added that the day before the pictures were taken, the photographer was "at the private home of the claimants" and said he was "casing their home, testing his light meter and taking photos through the security fence, so he was not at the park by accident".
Barnes stated that Splash's solicitors suggested that "the first claimant [Meghan] knew everything that was going on and was a volunteer in the sense that she carried on walking when she knew she was being photographed".
The Master, Victoria McCloud then gave the claimants permission to serve their case against the US arm of Splash.
The action is the latest taken by the couple against media outlets, with Meghan suing Associated Newspapers, publisher of The Mail On Sunday and MailOnline, over the publication of a letter she wrote to her estranged father, Thomas Markle.
