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We present an analysis of the effect of feedback from O- and B-type stars with data from the integral field spectrograph Multi Unit Spectroscopic Explorer (MUSE) mounted on the Very Large Telescope of pillar-like structures in the Carina Nebular Complex, one of the most massive star-forming regions in the Galaxy. For the observed pillars, we compute gas electron densities and temperatures maps, produce integrated line and velocity maps of the ionized gas, study the ionization fronts at the pillar tips, analyse the properties of the single regions, and detect two ionized jets originating from two distinct pillar tips. For each pillar tip, we determine the incident ionizing photon flux Q_0, pil_ originating from the nearby massive O- and B-type stars and compute the mass-loss rate {dot}M of the pillar tips due to photoevaporation caused by the incident ionizing radiation. We combine the results of the Carina data set with archival MUSE data of a pillar in NGC 3603 and with previously published MUSE data of the Pillars of Creation in M16, and with a total of 10 analysed pillars, find tight correlations between the ionizing photon flux and the electron density, the electron density and the distance from the ionizing sources, and the ionizing photon flux and the mass-loss rate. The combined MUSE data sets of pillars in regions with different physical conditions and stellar content therefore yield an empirical quantification of the feedback effects of ionizing radiation. In agreement with models, we find that {dot}M∝Q_0,pil^{1/2}.