We present results from integral field spectroscopy of a field located near the Trapezium Cluster using the Potsdam Multi-Aperture Spectrophotometer (PMAS). The observed field contains a variety of morphological structures: five externally ionized protoplanetary discs (also known as proplyds), the high-velocity jet HH 514 and a bowshock. Spatial distribution maps are obtained for different emission line fluxes, the c(Hβ) extinction coefficient, electron densities and temperatures, ionic abundances of different ions from collisionally excited lines (CELs), C2 + and O2 + abundances from recombination lines (RLs) and the abundance discrepancy factor of O2 +, ADF(O2 +). We distinguish the three most prominent proplyds (177-341, 170-337 and 170-334) and analyse their impact on the spatial distributions of the above mentioned quantities. We find that collisional de-excitation has a major influence on the line fluxes in the proplyds. If this is not properly accounted for then physical conditions deduced from commonly used line ratios will be in error, leading to unreliable chemical abundances for these objects. We obtain the intrinsic emission of the proplyds 177-341, 170-337 and 170-334 by a direct subtraction of the background emission, though the last two present some background contamination due to their small sizes. A detailed analysis of 177-341 spectra making use of suitable density diagnostics reveals the presence of high-density gas (3.8 × 105 cm-3) in contrast to the typical values observed in the background gas of the nebula (3800 cm-3). We also explore how the background subtraction could be affected by the possible opacity of the proplyd and its effect on the derivation of physical conditions and chemical abundances of the proplyd 177-341. We construct a physical model for the proplyd 177-341 finding a good agreement between the predicted and observed line ratios. Finally, we find that the use of reliable physical conditions returns an ADF(O2 +) about zero for the intrinsic spectra of 177-341, while the background emission presents the typical ADF(O2 +) observed in the Orion nebula (0.16 ± 0.11 dex). We conclude that the presence of high-density ionized gas is severely affecting the abundances determined from CELs and, therefore, those from RLs should be considered as a better approximation to the true abundances. Based on observations collected at the Centro Astronómico Hispano Alemán (CAHA) at Calar Alto, operated jointly by the Max-Planck Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC).