  We present a lattice QCD study of the contribution of the isovector quark
chromo-electric dipole moment (qcEDM) operator to the nucleon electric dipole
moments (nEDM). The calculation was carried out on four 2+1+1-flavor of highly
improved staggered quark (HISQ) ensembles using Wilson-clover quarks to
construct correlation functions. This clover-on-HISQ formulation is not fully
$O(a)$ improved, and gives rise to additional systematics over and above those
due to removing excited state contributions to getting ground-state matrix
elements, and the final chiral and continuum extrapolations to get the physical
result. We use the non-singlet axial Ward identity including corrections up to
$O(a)$ to show how to control the power-divergent mixing of the isovector qcEDM
operator with the lower dimensional pseudoscalar operator. The residual
corrections are observed to give rise to $O(25\%)$ violations in relations
arising from the axial Ward identity. We devise three methods attempting to
control the resulting uncertainty in the CP violating form factor; each of
these, however, can have large $O(a^2)$ corrections. Preliminary results for
the nEDM due to qcEDM are presented choosing the method giving the most uniform
behavior.
