Aims. Gas-phase metallicities offer insight into the chemical evolution of galaxies as they reflect the recycling of gas through star formation and galactic inflows and outflows. Environmental effects such as star-formation quenching mechanisms play an important role in shaping the evolution of galaxies. Clusters of galaxies at z<0.5 are expected to be the sites where environmental effects can be clearly observed with present-day telescopes. Methods. We explored the Frontier Fields cluster RX J2248-443 at z=0.348 with VIMOS/VLT spectroscopy from CLASH-VLT, which covers a central region corresponding to almost 2 virial radii. The fluxes of [OII]{lambda}3727, H{beta}, [OIII]{lambda}5007, H{alpha} and [NII]{lambda}6584 emission lines were measured allowing the derivation of (O/H) gas metallicities, star formation rates based on extinction-corrected H{alpha} fluxes, and contamination from active galactic nuclei. We compared our sample of cluster galaxies to a population of field galaxies at similar redshifts. Results. We use the location of galaxies in projected phase-space to distinguish between cluster and field galaxies. Both populations follow the star-forming sequence in the diagnostic diagrams, which allow the ionising sources in a galaxy to be disentangled, with only a low number of galaxies classified as Seyfert II. Both field and cluster galaxies follow the "main sequence" of star-forming galaxies, with no substantial difference observed between the two populations. In the mass-metallicity (MZ) plane, both high-mass field and cluster galaxies show comparable (O/H)s to the local SDSS MZ relation, with an offset of low-mass galaxies (log(M/M_{sun})<9.2) towards higher metallicities. While both the metallicities of "accreted" (RR_500) cluster members are comparable at all masses, the cluster galaxies from the "mass complete" bin (which is the intermediate mass bin in this study: 9.2<log(M/M_{sun}_)<10.2), show more enhanced metallicities than their field counterparts by a factor of 0.065 dex with a ~1.8{sigma} significance. The intermediate-mass field galaxies are in accordance with the expected (O/H)s from the fundamental metallicity relation, while the cluster members deviate strongly from the model predictions, namely by a factor of ~0.12dex. The results of this work are in accordance with studies of other clusters at z<0.5 and favour the scenario in which the hot halo gas of low- and intermediate-mass cluster galaxies is removed due to ram pressure stripping, leading to an increase in their gas-phase metallicity.