Aims. We present a study of the quiescent optical counterpart of the accreting millisecond X-ray pulsar XTE J1814-338 that is aimed at unveiling the different components, which contribute to the quiescent optical emission of the system. Methods. We carried out multiband (BVR) orbital phase-resolved photometry of the system using the ESO Very Large Telescope (VLT) that is equipped with the FORS2 camera, covering about 70% of the 4.3 hour orbital period. Results. The optical light curves are consistent with a sinusoidal variability that are modulated with an orbital period with a semiamplitude of 0.5−0.7 mag. They show evidence of a strongly irradiated companion star, which agrees with previous findings for this system. However, the observed colours cannot be accounted for by the companion star alone, suggesting the presence of an accretion disc during quiescence. The system seems to be 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 curve performed with a Markov chain Monte Carlo technique, we derive constraints on the companion star, disc fluxes, system distance, and companion star mass. Conclusions. 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. Compared to our data with previous observations, which were collected over 5 years, the flux decrease and spectral evolution of the observed quiescent optical emission cannot be satisfactorily explained with the combined contribution of an irradiated companion star and of an accretion disc alone. The observed progressive flux decrease as the system gets bluer could be due to a continuum component that evolves 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 significantly contributing in the data obtained earlier during quiescence and then progressively fading or moving its break frequency towards longer wavelengths.