  We present a study of the quiescent optical counterpart of the Accreting
Millisecond X-ray Pulsar XTE J1814-338, carrying out multiband (BVR) orbital
phase-resolved photometry using the ESO VLT/FORS2. The optical light curves are
consistent with a sinusoidal variability modulated with the orbital period,
showing evidence for a strongly irradiated companion star, in agreement with
previous findings. The observed colours cannot be accounted for by the
companion star alone, suggesting the presence of an accretion disc during
quiescence. The system is fainter in all analysed bands compared to previous
observations. The R band light curve displays a possible phase offset with
respect to the B and V band. Through a combined fit of the multi-band light
curves we derive constraints on the companion star and disc fluxes, on the
system distance and on the companion star mass. The irradiation luminosity
required to account for the observed day-side temperature of the companion star
is consistent with the spin-down luminosity of a millisecond radio pulsar. The
flux decrease and spectral evolution of the quiescent optical emission observed
comparing our data with previous observations, collected over 5 years, cannot
be well explained with the contribution of an irradiated companion star and an
accretion disc alone. The progressive flux decrease as the system gets bluer
could be due to a continuum component evolving towards a lower, bluer spectrum.
While most of the continuum component is likely due to the disc, we do not
expect it to become bluer in quiescence. Hence we hypothesize that an
additional component, such as synchrotron emission from a jet was contributing
significantly in the earlier data obtained during quiescence and then
progressively fading or moving its break frequency toward longer wavelengths.
