Hi, Genie!
Gail Gardner's friend, Billy Simon, wrote the music for Gardner's poem, Sierry Petes. The sheet music is shown in Ohrlin, Glenn, The Hell-Bound Train, pp. 69-70. Katie Lee, in Ten Thousand Goddam Cattle, also credits Simon with the music, but the fragment she gives (p. 225) is slightly different from that in Ohrlin.
The music in John White 's book, Git Along Little Dogies, has been modified to suit White's voice; it differs from the one in Ohrlin and the one in Lee; I would guess that Ohrlin's is the real one but he also could have modified a note or several to suit HIS voice and interpretation.
The stolen and revised song, "Tying Knots," as sung by other singers, could have other revisions.
Genie, take your pick to suit your voice, but I hope you sing Sierry Petes, not Tying Knots.

Lomax, a collector but sloppy in his documentation (definitely not familiar with research), printed "Tying a Knot..." in his American Ballads and Folk Songs, but did not acknowledge Gardner as the author, creating resentment on the part of Gardner and others who knew the true story.