  The calculation of the neutron electric dipole moment within effective field
theories for physics beyond the Standard Model requires non-perturbative
hadronic matrix elements of effective operators composed of quark and gluon
fields. In order to use input from lattice computations, these matrix elements
must be translated from a scheme suitable for lattice QCD to the
minimal-subtraction scheme used in the effective-field-theory framework. The
accuracy goal in the context of the neutron electric dipole moment necessitates
at least a one-loop matching calculation. Here, we provide the one-loop
matching coefficients for the $CP$-odd three-gluon operator between two
different minimally subtracted 't Hooft-Veltman schemes and the gradient flow.
This completes our program to obtain the one-loop gradient-flow matching
coefficients for all $CP$-violating and flavor-conserving operators in the
low-energy effective field theory up to dimension six.
