We continue the exploration of the BaLROG (Bars in Low Redshift Optical Galaxies) sample: 16 large mosaics of barred galaxies observed with the integral field unit Spectrographic Areal Unit for Research on Optical Nebulae. We quantify the influence of bars on the composition of the stellar component. We derive line-strength indices of H β, Fe5015 and Mgb. Based on single stellar population (SSP) models, we calculate ages, metallicities and [Mg/Fe] abundances and their gradients along the bar major and minor axes. The high spatial resolution of our data allows us to identify breaks among index and SSP profiles, commonly at 0.13 ± 0.06 bar length, consistent with kinematic features. Inner gradients are about 10 times steeper than outer gradients and become larger when there is a central rotating component, implying that the gradients are not independent of dynamics and orbits. Central ages appear to be younger for stronger bars. Yet, the bar regions are usually old. We find a flattening of the iron (Fe5015) and magnesium (Mgb) outer gradients along the bar major axis, translating into a flattening of the metallicity gradient. This gradient is found to be 0.03 ± 0.07 dex kpc-1 along the bar major axis while the mean value of the bar minor axis compares well with that of an unbarred control sample and is significantly steeper, namely -0.20 ± 0.04 dex kpc-1. These results confirm recent simulations and discern the important localized influence of bars. The elevated [Mg/Fe] abundances of bars and bulges compared to the lower values of discs suggest an early formation, in particular for early-type galaxies.