[7] To assist Hopkin in learning the song, McCartney recorded a solo demo at his home, 7 Cavendish Avenue, London, in early February 1969.

The song was arranged by Richard Hewson, who had also orchestrated "Those Were the Days,"[9] and produced, along with its flip side, "Sparrow", by Paul McCartney on 1 March 1969 at Morgan Studios in Willesden.

In the footage, Hopkin can be seen miming to the song inside the studio, combined with shots of her and McCartney in the control room listening to a playback.

[11] The flip side "Sparrow" was written by Benny Gallagher and Graham Lyle, a songwriting duo signed to Apple Publishing.

[13] Mary Hopkin met her future husband, record producer Tony Visconti, while making foreign-language versions of the song.

"[19] Allmusic critic Richie Unterberger described "Goodbye" as a "pleasant and catchy romp, rather like a Continental European folk love ballad in tone, with a dash of music hall.

[21] The international online magazine PopMatters published McCartney's demo along with critical commentary expressing a preference for the composer's version over Hopkin's rendition.