"Do you need help with the photoshop guys?," another said.
"The photoshop on this is horrific, not being funny it's the queen surely they could have got someone to do a better job than that," one added.
The couple have rarely been photographed together since the Duke retired from public life in 2017.
He was last seen publicly leaving a London hospital on Christmas Eve after being treated for a pre-existing condition, and released a rare public statement in April to thank those fighting on the frontline against COVID-19.
Meanwhile, Queen Elizabeth was pictured just last week, with the palace releasing photos of Her Majesty riding a horse in the grounds of Windsor Castle.
The Duke will spend his birthday at Windsor Castle with the 94-year-old monarch.
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While the royal couple continue their self-imposed isolation, the rest of their family will have to send their best wishes to Prince Philip by video calls, and the London gun salute will not go ahead. The Queen cancelled such tributes for her own birthday in April for the first time in her 68-year reign.
"I haven't seen my father for a long time. He's going to be 99 next week," heir-to-the-throne Prince Charles said last week.
"FaceTime is all very well … You really want to give people a hug."
Prince Philip and the Queen married in 1947, when Philip was 26 and the monarch was 21.