The growing sample of LIGO-Virgo black holes (BHs) opens new perspectives for the study of massive binary evolution. Here, we study the impact of mass accretion efficiency on the properties of binary BH (BBH) mergers, by means of population synthesis simulations. We model mass accretion efficiency with the parameter fMT∈[0.05,1], which represents the fraction of mass lost from the donor which is effectively accreted by the companion. Lower values of fMT result in lower BBH merger rate densities and produce mass spectra skewed towards lower BH masses. Our hierarchical Bayesian analysis, applied to BBH mergers in the first and second observing run of LIGO-Virgo, yields almost zero support for values of fMT≤0.3. This result holds for all the values of the common-envelope efficiency parameter we considered in this study (αCE=1, 5 and 10). The lower boundaries of the 95% credible intervals are equal to fMT=0.40,0.45 and 0.48 for αCE=1, 5 and 10, respectively. This confirms that future gravitational-wave data can be used to put constraints on several uncertain binary evolution processes.