Although The Supremes' song Where Did Our Love Go, which the girls are singing along to in May 1964, was recorded on April 8, it wasn't released as a single until June 17 and later, on August 31, as an album.
Sister Margaret (Georgann Johnson) tells Vera and Valens what Karen (Michelle Page) and Hilary (Johanna Braddy) said after they'd put their fake wedding bands on. But she had already left them and gone inside, so she couldn't have heard the conversation.
The girls are singing into a cassette tape recorder in May 1964, but cassette tape recorders were not commercially available in the US until after June 1964.