“Old rocker who can not sell enough tickets to their last gig need publicity,” Mr. Palmer wrote in a text message to Australia’s ABC News on Wednesday.

He, too, threatened to sue.

“I wrote the words personally that appear on our promotion and hold the copyright for those words,” The Sydney Morning Herald quoted Mr. Palmer as saying.

If members of the band “attempt to use my lyrics in any of their songs, I’ll not hesitate to take legal proceedings against them,” he said. “As foreigners, they should stay out of Australian domestic politics and stay where they are. Aussies are not going to cop it at all!”

This is not the first time Twisted Sister has clashed with politicians about the song, which, when it was released in 1984, struck a chord with its themes of rebellion and freedom of choice.

Paul D. Ryan, the outgoing speaker of the United States House of Representatives, used it during his vice-presidential run with former Gov. Mitt Romney of Massachusetts in 2012. Mr. Snider’s statement at the time denouncing Mr. Ryan’s use of the song included the comment: “There is almost nothing on which I agree with Paul Ryan, except perhaps the use of the P90X,” referring to Mr. Ryan’s workout program.

Mr. Snider did, however, allow Donald Trump to use the song in his presidential campaign. Mr. Snider told Newsweek that Mr. Trump was a friend and had asked him for permission, which he gave because Mr. Trump’s “rebelling” was in the song’s spirit. (Mr. Snider has since said that he was “not a fan of Trump’s style,” though he said the president was “not being given a chance.”)