I believe the first US singer to introduce "Delia's Gone" (by that title) to American folk circles was Pete Seeger on a Folkways 10" LP, album title not remembered, in the early 1950s.
His version uses the Blind Blake refrain (as compared to the several others that use different refrains) but the lyrics are condensed and somewhat different. Whether the divergencies are recomposition by Seeger or are due to some intermediate party I don't know.
The Seeger version was enormously influential at the time. Blake's quite popular Behamian recordings reached the US via tourists, but were much less widely heard.