  Contrary to conformal transformations, disformal transformations can change
the principal null directions of a spacetime geometry. Thus, depending on the
frame a gravitational wave (GW) detector minimally couples to, the properties
of GWs may change. In this letter, we provide necessary and sufficient
conditions which determine whether GWs change under disformal transformations
or not. Our argument is coordinate-independent and can be applied to any
spacetime geometry at the fully non-linear level. As an example, we show that
an exact solution of Einstein-scalar gravity exhibiting only a breathing scalar
mode acquires non-linear superposition of the breathing mode and tensorial GWs
in the disformed frame. This type of non-linear effect can be completely
overlooked in the usual linear perturbation theory.
