  An important aspect of quenching star formation is the removal of the cold
interstellar medium (ISM; non-ionised gas and dust) from a galaxy. In addition,
dust grains can be destroyed in a hot or turbulent medium. The adopted
timescale of dust removal usually relies on uncertain theoretical estimates. It
is tricky to track the dust removal, because usually dust is constantly
replenished by consecutive generations of stars. Our objective is to measure
observationally the timescale of dust removal. We here explore an approach to
select galaxies which do have detectable amounts of dust and cold ISM but
exhibit a low current dust production rate. Any decrease of the dust and gas
content as a function of the age of such galaxies therefore must be attributed
to processes governing the ISM removal. We used a sample of galaxies detected
by Herschel in the far-infrared with visually assigned early-type morphology or
spirals with red colours. We also obtained JCMT/SCUBA-2 observations for five
of them. We discovered an exponential decline of the dust-to-stellar mass ratio
with age, which we interpret as an evolutionary trend of dust removal from
these galaxies. For the first time we directly measure the dust removal
timescale in such galaxies to be tau=(2.5+-0.4) Gyr (the corresponding
half-life time is (1.75+-0.25) Gyr). This quantity may be used in models in
which it must be assumed a priori and cannot be derived. Any process which
removes dust in these galaxies, such as dust grain destruction, cannot happen
on shorter timescales. The timescale is comparable to the quenching timescales
found in simulations for galaxies with similar stellar masses. The dust is
likely of internal, not external origin. It was either formed in the past
directly by supernovae, or from seeds produced by SNe and with grain growth in
the ISM contributing substantially to the dust mass accumulation.
