Volker Bertelmann, Carter Burwell and Son Lux are also nominated for original score.
The singer died on Jan. 15 after being rushed to the hospital in his native Alabama.
Swift took the stage at the band's concert at The U.K.'s O2 venue last week to perform their 2013 single.
The alternative greats' 1987 classic was featured as a message of "trouble" in the new HBO series' pilot episode.
"Your new song carries the torch of empowerment," Gaynor wrote to Cyrus.
The Jamieson Shaw Remix, from the film "Elvis," is a mash-up of Presley's "Viva Las Vegas" and Spears' "Toxic."
"You would never think that our paths would really cross," explained the Stranger Things actress on Late Night With Seth Meyers.
The Queen of Country's best solo songs to date, from "9 to 5" to "Jolene."
The singer-songwriter achieves her fourth career-starting top 10.
The video also reveals the next single that will arrive off upcoming album The First Time.
