"dispute the interpretation" is a perfectly valid phrase to use in written English.
You may use it when you want to express disagreement with an interpretation of something, or to suggest that an interpretation should be reconsidered. For example: "John argued that the painting was a reflection of the artist's feelings, but I disputed the interpretation."
I don't dispute the findings, but I dispute the interpretation of them," he told The Huffington Post.
He aligns himself with scientists who contend that current findings dispute the interpretation of the Cambrian "explosion" that Stephen Jay Gould subscribed to in his popular 1988 book, "Wonderful Life".
Arsenal made a club-record offer of £40m plus £1 for Suarez in the belief it would enable them to secure his services, but Liverpool dispute the interpretation of a clause in his contract.
While the regulations have generated a considerable amount of work for the Federal Court of Canada both sides dispute the interpretation of the "win rate" in the court cases.
State officials dispute the interpretations of the tenant groups and say they are prepared to defend the codes in court.
Secondly, they say Ahmad disputes the interpretation the Sun has placed on his conversation with its member of staff.
The former defence minister also disputed the interpretation of those who say the UN resolution was not clear authorisation for military action against Isis.
Critics disputed the interpretation, saying this was not clear evidence for the existence of a separate species, known as Homo floresiensis.
Defence lawyer Michael Gleeson told the court that Gsubramaniam had no criminal record, had entered the country legally and on his own passport and disputed the interpretation of the police recordings.
His next famous case was Chudleigh's Case, a dispute over the interpretation of the Statute of Uses, followed by Slade's Case, a dispute between the Common Pleas and King's Bench over assumpsit now regarded as a classic example of the friction between the two courts and the forward movement of contract law; Coke's argument in Slade's Case formed the first definition of consideration.
In his meta-methodology, Feyerabend applied to the dispute over the interpretation of scientific theories a strong measure of Popperian methodological conventionalism, arguing that the dispute between realists and instrumentalists is not a factual issue but a matter of choice.
