  The important issue of the magnetic component of gravitational waves (GWs)
has been considered in various papers in the literature. From such analyses, it
resulted that such a magnetic component becomes particularly important in the
high frequency portion of the frequency range of ground based interferometers
for GWs which arises from standard General Theory of Relativity (GTR).
Recently, such a magnetic component has been extended to GWs arising from
Scalar-Tensor Gravity (STG) too. After a review of some important issues on GWs
in STG, in this paper we re-analyse the magnetic component in the framework of
STG from a different point of view, by correcting an error in a previous paper
and by releasing a more precise response function. In this way, we also show
that if one neglects the magnetic contribution considering only the
low-frequency approximation of the electric contribution, an important part of
the signal could be, in principle, lost. The determination of a more precise
response function for the magnetic contribution is important also in the
framework of the possibility to distinguish other gravitational theories from
GTR. At the end of the paper an expansion of the main results is also shown in
order to recall the presence of the magnetic component in GRT too.
