Laurie Metcalf revealed on an interview that she took the job because one of her daughters is a huge fan of the show.
The title is a pun on the phrase "shot through the heart", which is also the first line of Bon Jovi's first #1 hit, "You Give Love a Bad Name". It was previously mentioned in "Legion of Super-Heroes (2018)" that, after a catastrophic extinction of life and culture in the future, Bon Jovi's music was one of numerous things in Earth's history about which Mon-El told the Legion; to convince him that Kara needs their help, Imra also quotes their second #1 hit, "Livin' on a Prayer", and the song itself is played over the Legion's face-off with Reign.
Near the end of the episode, Mon-El sings Carry on Wayward Son by Kansas. The song is the unofficial theme song of fellow CW show Supernatural (2005). Since season 2, it has played at the start of each season finale during the season recap and Kansas performed the song live before Supernatural (2005)'s panel at San Diego Comic-Con in 2017.
Guest star Laurie Metcalf also has a recurring guest star role on "The Big Bang Theory (2007)" as Mary Cooper, Sheldon Cooper's (Jim Parsons) mother. Sheldon is a huge fan of DC comics. The show "Supergirl (2015)" is based on DC Comics characters.
The cast knew the karaoke scene was coming, however, it wasn't scripted. The crew told them that they could come up with their own song, and sing it how they choose.