  Recently, an action principle for the $D\rightarrow4$ limit of the
Einstein-Gauss-Bonnet gravity has been proposed. It is a special scalar-tensor
theory that belongs to the family of Horndeski gravity. It also has a well
defined $D\rightarrow3$ and $D\rightarrow2$ limit. In this work, we examine
this theory in three and four dimensions in Bondi-Sachs framework. In both
three and four dimensions, we find that there is no news function associated to
the scalar field, which means that there is no scalar propagating degree of
freedom in the theory. In four dimensions, the mass-loss formula is not
affected by the Gauss-Bonnet term. This is consistent with the fact that there
is no scalar radiation. However, the effects of the Gauss-Bonnet term are quite
significant in the sense that they arise just one order after the integration
constants and also arise in the quadrupole of the gravitational source.
