  Context. Thanks to the high-precision photometry from space missions such as
Kepler and TESS, tidal perturbations and tilting of pulsations have been
detected in more than a dozen binary systems. However, only two of these were
g-mode pulsators. Aims. We aim to detect tidally perturbed g modes in
additional binary systems and characterise them observationally. Methods. We
perform a custom data reduction of the available Kepler and TESS photometry of
a well-studied sample of 35 binary systems with gamma Doradus pulsators. For
each target, we model the binary signal using a sum of 100 sine waves, with
frequencies at orbital harmonics, and measure significant pulsation frequencies
by iteratively prewhitening the residual light curve. Pulsations are labelled
as tidally perturbed g modes if they are part of both period-spacing patterns
and orbital-frequency-spaced multiplets. After visual inspection and
confirmation, the properties of these targets and g modes are characterised.
Results. We detect tidally perturbed g-mode pulsations for five short-period
binaries that are circularised and (almost) synchronously rotating: KIC3228863,
KIC3341457, KIC4947528, KIC9108579, and KIC12785282. Tidally perturbed g modes
that occur within the same star and have the same mode identification (k,m),
are found to have near-identical relative amplitude and phase modulations,
which are within their respective 1-sigma uncertainties also identical for the
Kepler and TESS photometric passbands. By contrast, pulsations with different
mode identification (k,m) are found to exhibit different modulations. Moreover,
the observed amplitude and phase modulations are correlated, indicating that
the binary tides primarily distort g-mode amplitudes on the stellar surface.
The phase modulations are then primarily a geometric effect of the integration
of the stellar flux over the visible stellar surface. (abbreviated)
