I have encountered "The Love Song of J. Alfred Poofrock" in three different college English classes taught by three different teachers. They all agree that T. S. Eliot wrote the poem. On everything else they disagree.
"The Hairy Arms Poem or The Love Song of J. Alfred Poofrock,"
Manuscripts: Vol. 42
, Article 7.
Available at: https://digitalcommons.butler.edu/manuscripts/vol42/iss1/7