The main characters are ex-astronaut Jeff Tracy, founder of International Rescue, and his five adult sons, who pilot the organisation's primary fleet of vehicles: the Thunderbird machines.
While holidaying in France, International Rescue agent Lady Penelope finds an old acquaintance – Deborah, Duchess of Royston – losing heavily at a casino.
Unaware that criminals Brophy and Chandler are eavesdropping, Deborah tells Penelope that she has been driven gambling after "falling on hard times" and has already lost most of her possessions.
When Deborah lands, Brophy, posing as Hendricks, drives her to an abandoned country house, ties her to a chair in the basement, switches on a leaking gas supply and leaves her to suffocate.
However, he is unaware that Penelope has warned Dandridge to expect an impostor, having tracked Deborah's movements using a homing device hidden inside a St Christopher brooch that she gave the Duchess as a present.
While Virgil tunnels down to the burning basement in the Mole, Scott uses the DOMO (Demolition and Object Moving Operator) to hold up the house's one surviving wall.
Dandridge believes Portrait of a Gazelle to be irreparably damaged, but to everyone's amazement, Deborah unscrews the handle of her umbrella to reveal the painting rolled up inside – the canvas that travelled to New York was a copy.
[1] Stephen La Rivière writes that "The Duchess Assignment" has an "enjoyable, quirky charm", praising aspects such as the design of the Deborah puppet and describing the story in general as "one of the most unusual episodes in the Anderson canon".
[7] Michael Coldwell praises Elliott's "assured direction" and art director Bob Bell's "outstanding" set design, as well as the script's "balance of action, futuristic technology and distinctively quirky characterisation".
Coldwell also suggests that the episode's "Ealing Comedy set-up" demonstrates Gerry Anderson's "affection for English eccentricity" and argues that International Rescue's reduced role shows "just how well Lady Penelope and Parker could have carried their own series".
He notes that Deborah's destitution is partly the result of gambling addiction: "another of the adult vices that makes a surprise appearance in a series ostensibly aimed at children.
"[17] He believes that the costume worn by the Penelope puppet in the art gallery scene – a dress presenting blocks of white and red with black borders – was inspired by the work of Piet Mondrian.
[20] John Peel notes that in the closing scene at the hospital, the wall next to Deborah's bed features a panel called "Auto-Nurse" that monitors patients' vital signs, which he describes as "almost a duplicate" of a device seen in Star Trek: The Original Series.