Amelia Lily performed the band's 1987 hit 'China in Your Hand' during the show, prompting Barlow to quip that it was nice to hear the song being sung in tune for once.
"Gary Barlow you t**t! & I had to suffer a Take That concert for the sake of my kids this summer," Decker wrote on her Twitter page.
She then tweeted Barlow directly, asking: "What's your f**king problem? I actually have perfect pitch."
'China in Your Hand', which was written by Decker, was on T'Pau's album Bridge of Spies and spent five weeks at number one following its release.
The X Factor contestants are performing two tracks tonight as they battle it out for a place in next weekend's semi-final.
Watch T'Pau's video for 'China in Your Hand' below:
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