The quasiparticle random phase approximation is used to study the properties of the wobbling bands in $^{163}$Lu. Assuming that the wobbling mode represents pure isoscalar orientation oscillations results in too low wobbling frequencies and too strong M1 transitions between the one- and zero-phonon wobbling bands. The inclusion of an LL interaction, which couples the wobbling mode to the scissors mode, generates the right upshift of the wobbling frequencies and the right suppression of the B(M1)$_{out}$ values toward the experimental values. In analogy to the quenching of low-energy E1 transition by coupling to the Isovector Giant Dipole Resonance, a general reduction of the M1 transitions between quasiparticle configurations caused by coupling to the scissors mode is suggested.
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