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We revisit the treatment of spurious ultraviolet divergences in the equation ofmotion of the gluon propagator caused by a momentum cutoff and the resulting violation of gauge invariance. With present continuum studies of the gluon propagator from its DysonSchwinger equation reaching the level of quantitatively accurate descriptions, it becomes increasingly important to understand how to subtract these spurious divergences in an unambiguous way. Here we propose such a method. It is based entirely on the asymptotic perturbative behavior of the QCD Green’s functions without affecting non-perturbative aspects such as mass terms or the asymptotic infrared behavior. As a particular example, this allows us to assess the possible influence of the tadpole diagram beyond perturbation theory. Finally, we test this method numerically by solving the system of Dyson-Schwinger equations of the gluon and ghost propagators.