At least on the web, "kiss" is given as original, but I am sure I
remember reading the other at some point. No sure where; I think "kiss"
was what he published. N.
We crossed with this information: it's called "The Ball of Kerrymuir" and is pretty well known in Scotland. But as I noted before, it is part of a long oral tradition and particularly of Bothy Ballads--many oral songs and traditions have some factual (or claimed factual) origins. Ironically, the main version on the web is made nice--all the "f" words cut. They did the same to Burns; it was not originally "gin a body kiss a body/ comin' through the rye."
Eliot mentions Burns someplace in a sort of condescending way if I remember correctly. But he could no more match Burns in bawdy than he could match Pope in couplets. I know nothing of the publishing history of Burns -- when and where his bawdy got published. I wonder if Eliot had any knowledge of it.