  In this paper we explore how different regularization prescriptions affect
the counterterms in the renormalization of the galaxy bias expansion. We work
in the context of primordial local non-Gaussianity including non-linear
gravitational evolution. We carry out the one-loop renormalization of the field
$\delta_\rho^2$ (i.e. the square of the matter overdensity field) up to third
order in gravitational evolution. Three regularization schemes are considered
and their impact on the values of the counterterms is studied. We explicitly
verify that the coefficients of the non-boost invariant operators are
regularization scheme independent.
