  Alternative theories of gravity may be put to the test by making use of
gravitational wave observations. Scalar-tensor theories provide a relatively
simple framework that allows for compact object solutions with characteristics
different from those of their GR counterparts. In shift-symmetric theories,
black hole hair may arise when a linear coupling with the Gauss-Bonnet (GB)
invariant is introduced. The effect of this coupling on the black hole
quasinormal modes (QNMs) has been shown to be small, therefore limiting the
observational interest in the theory. In general, however, one expects that
additional shift-symmetric terms in the Lagrangian may be relevant, and indeed,
it has been shown that they can have a nontrivial impact on the mass and scalar
charge of the stationary solutions. In this work we explore the effect that
various such terms have on the axial and polar QNMs of the hairy black hole
solutions.
