  We consider the extended SU(3) Nambu and Jona-Lasinio model with explicit
vector couplings in the presence of external fields. We study the chiral
anomaly in this model and its implications on the properties of the nucleon
described as a chiral soliton of three valence quarks bounded in mesonic
background fields. For the model to reproduce the QCD anomaly it is necessary
to subtract suitable local and polynomial counterterms in the external and
dynamical vector and axial-vector fields. We compute the counterterms
explicitly in a vector gauge invariant regularization, and obtain modifications
to the total effective action and vector and axial currents. We study the
numerical influence of those counterterms in the two flavour version of model
with dynamical $\sigma,\pi, \rho, A $ and $\omega$ mesons. We find that, for
time independent hedgehog configurations, the numerical effects in the nucleon
mass, the isoscalar nucleon radius and the axial coupling constant are
negligibly small.
