Corrections to scaling in the 3D Ising model are studied based on Monte Carlo (MC) simulation results for very large lattices with linear lattice sizes up to L=3456. Our estimated values of the correction-to-scaling exponent ω tend to decrease below the usually accepted value about 0.83 when the smallest lattice sizes, i.e. L<Lmin with Lmin [6,64], are discarded from the fits. This behavior apparently confirms some of the known estimates of the Monte Carlo renormalization group (MCRG) method, i.e. ω≈0.7 and ω=0.75(5). We discuss the possibilities that ω is either really smaller than usually expected or these values of ω describe some transient behavior which, eventually, turns into the correct asymptotic behavior at Lmin>64. We propose refining MCRG simulations and analysis to resolve this issue. Our actual MC estimations of the critical exponents η and ν provide stable values η=0.03632(13) and ν=0.63017(31), which well agree with those of the conformal bootstrap method, i.e. η=0.0362978(20) and ν=0.6299709(40).