We investigate how the way galaxies acquire their gas across cosmic time in cosmological hydrodynamic simulations is modified by a comprehensive physical model for baryonic feedback processes. To do so, we compare two simulations -with and without feedback -both evolved with the moving mesh code AREPO. The feedback runs implement the full physics model of the Illustris simulation project, including star formation driven galactic winds and energetic feedback from supermassive blackholes. We explore: (a) the accretion rate of material contributing to the net growth of galaxies and originating directly from the intergalactic medium, finding that feedback strongly suppresses the raw, as well as the net, inflow of this "smooth mode" gas at all redshifts, regardless of the temperature history of newly acquired gas. (b) At the virial radius the temperature and radial flux of inflowing gas is largely unaffected at z = 2. However, the spherical covering fraction of inflowing gas at 0.25 r vir decreases substantially, from more than 80% to less than 50%, while the rates of both inflow and outflow increase, indicative of recycling across this boundary. (c) The fractional contribution of smooth accretion to the total accretion rate is lower in the simulation with feedback, by roughly a factor of two across all redshifts. Moreover, the smooth component of gas with a cold temperature history, is entirely suppressed in the feedback run at z < 1. (d) The amount of time taken by gas to cross from the virial radius to the galaxy -the "halo transit time" -increases in the presence of feedback by a factor of 2 -3, and is notably independent of halo mass. We discuss the possible implications of this invariance for theoretical models of hot halo gas cooling.