Rabie Darduna told the BBC he was given less than $175 for the image drawn on the only remaining door of his house in Gaza.
Banksy visited Gaza in February and used the rubble as a canvas for his graffiti.
His paintings included a cat playing with a ball of mangled metal and an image of children swinging from an Israeli watchtower. On the door of the Dardunas’ ruined house, he painted a picture of a weeping Greek goddess.
Darduna said he was duped into selling the piece by a local man who was pretending to work for the artist.
The buyer said his purchase was legal. He said he paid $175 for the mural. But Banksy’s artworks usually carry a much higher price tag.
In August 2014, a painting by the artist left on the wall of a social club in the English city of Bristol sold for more than $590,000.
Banksy’s representative has contacted them to say the artist believes the picture should be returned.
Banksy is the pseudonym of an British graffiti artist, political activist, film director, and painter.