  We examine conservation of the E7(7) Noether-Gaillard-Zumino current in the
presence of N=8 supergravity counterterms using the momentum space helicity
formalism, which significantly simplifies the calculations. The main result is
that the 4-point counterterms at any loop order L are forbidden by the E7(7)
current conservation identity. We also clarify the relation between linearized
and full non-linear superinvariants as candidate counterterms. This enables us
to show that all n-point counterterms at L=7, 8 are forbidden since they
provide a non-linear completions of the 4-point ones. This supports and
exemplifies our general proof in arXiv:1103.4115 of perturbative UV finiteness
of N=8 supergravity.
