The chorus of Taylor's new single Look What You Made Me Do follows the same rhythmic pattern as I'm Too Sexy.
After the song was released overnight, the duo tweeted: "Thank you Taylor Swift, what a marvellous reinvention!"
The group's spokesman confirmed to the BBC they were approached by Taylor's team in advance of the release.

Police are urging Prof Wyndham Lathem, 42, and Andrew Warren, 56, to "do the right thing and turn yourself in".
Arrests warrants were issued after Trenton Cornell-Duranleau, 25, was found dead in Prof Lathem's flat in Chicago on 27 July.
"The victim had several lacerations to the body," the police said.
Wyndham Lathem is a microbiology professor at Northwestern University in Illinois, who specialises in the bacteria that caused the bubonic plague.
Andrew Warren is a senior treasury assistant at Oxford's Somerville College.
The police warned that the suspects were believed to be "armed and dangerous", and were possibly driving a Hyundai sedan.
Chicago Police chief communications officer Anthony Guglielmi said on Twitter the search for the two men "will only intensify".
End of Twitter post  by @AJGuglielmi
Mr Cornell-Duranleau, originally from Michigan, worked as a cosmetologist in Chicago.
Oxford University issued a statement saying it had been in contact with the police in the UK about Mr Warren and was "ready to help the US investigating authorities in any way they need".
It added: "Andrew Warren's colleagues at Somerville College have now all been informed and are shocked to learn of the case.
"Whatever the circumstances, we would urge him to contact the US authorities as soon as possible, in the best interests of everyone concerned."
A Thames Valley Police spokesman said Mr Warren was reported missing on 25 July after having left the UK the day before.

Hammers manager Slaven Bilic said earlier this month that Payet did not want to play for the club, but added the 29-year-old would not be sold.
But, after rejecting two bids from Marseille and signing Robert Snodgrass, West Ham have decided to sell the France international.
Payet joined West Ham from Marseille for £10.7m in June 2015.
He excelled in his first season with the London club, scoring 12 goals and earning a nomination for the PFA Players' Player of the Year award.
In February 2016 he signed a new contract to tie him to the Hammers to the summer of 2021.
He then helped France reach the final of Euro 2016, where the hosts were beaten by Portugal.
However, Payet has scored just three goals for the Hammers this season.
Right Said Fred have been credited as writers on Taylor Swift's new single in one of the most bizarre musical combinations of the year.
[NEXT_CONCEPT]
A US-wide hunt has intensified for an American professor and an Oxford University employee suspected of stabbing a man to death in Chicago.
[NEXT_CONCEPT]
West Ham forward Dimitri Payet is set to rejoin former club Marseille after the clubs agreed a £25m fee.