In this letter, we revise the QED gauge invariance for the hadron tensor of Drell-Yan type processes with the transversely polarized hadron. We perform our analysis within the Feynman gauge for gluons and make a comparison with the results obtained within the light-cone gauge. We demonstrate that QED gauge invariance leads, first, to the need of a non-standard diagram and, second, to the absence of gluon poles in the correlators ⟨ψ¯γ⊥A+ψ⟩ related traditionally to dT(x,x)/dx. As a result, these terms disappear from the final QED gauge invariant hadron tensor. We also verify the absence of such poles by analysing the corresponding light-cone Dirac algebra.