The contribution of the three-body Coulomb dynamics of the transfer mechanism to the partial wave amplitudes at for the peripheral proton-transfer reaction 22Ne(3He,d)23Na is estimated within the three-body approach combining the dispersion method and the DWBA approach. For this reaction, the Coulomb renormalization factors, arising owing to correctly taking into account the three-body Coulomb dynamics of the proton-transfer mechanism in the DWBA cross sections, are calculated. A new estimate is obtained for the values of the asymptotic normalization coefficients for 22Ne+p→23Na, which also have astrophysical interest.