  In the framework of an arbitrary $D$-dimensional metric theory, perturbations
are considered on arbitrary backgrounds that are however solutions of the
theory. Conserved currents for perturbations are presented following two known
prescriptions: canonical N{\oe}ther theorem and Belinfante symmetrization rule.
Using generalized formulae, currents in the Einstein-Gauss-Bonnet (EGB) gravity
for arbitrary types of perturbations on arbitrary curved backgrounds (not only
vacuum) are constructed in an explicit covariant form. Special attention is
paid to the energy-momentum tensors for perturbations which are an important
part in the structure of the currents. We use the derived expressions for two
applied calculations: a) to present the energy density for weak flat
gravitational waves in $D$-dimensional EGB gravity; b) to construct the mass
flux for the Maeda-Dadhich-Molina 3D radiating black holes of a Kaluza-Klein
type in 6D EGB gravity.
