  Recently, the possibility of evading Lovelock's theorem at $d=4$, via a
singular redefinition of the dimensionless coupling of the Gauss-Bonnet term,
has been very extensively discussed in the cosmological context. The term is
added as a quadratic contribution of the curvature tensor to the
Einstein-Hilbert action, originating theories of "Einstein Gauss-Bonnet" (EGB)
type. We point out that the action obtained by the dimensional regularization
procedure, implemented with the extraction of a single conformal factor,
correspond just to an ordinary Wess-Zumino anomaly action, even though it is
deprived of the contribution from the Weyl tensor. We also show that a purely
gravitational version of the EGB theory can be generated by allowing a finite
renormalization of the Gauss-Bonnet topological contribution at $d= 4 +
\epsilon$, as pointed out by Mazur and Mottola. The result is an effective
action which is quadratic, rather then quartic, in the dilaton field, and scale
free, compared to the previous derivations. The dilaton, in this case can be
removed from the spectrum, leaving a pure gravitational theory, which is
nonlocal. We comment on the physical meaning of the two types of actions, which
may be used to describe such topological terms both below and above the
conformal breaking scale.
