Comment on "Frequency shifts in NIST Cs primary frequency standards due to transverse rf field gradients"

We discuss the theoretical treatment of the microwave lensing frequency shift of the NIST-F1 and F2 atomic fountain clocks by Ashby et al. [Phy. Rev. A. 91, 033624 (2015)]. The shifts calculated by NIST are much smaller than the previously evaluated microwave lensing frequency shifts of other clocks contributing to International Atomic Time. We identify several fundamental problems in the NIST treatment and demonstrate that each significantly affects their results. We also show a smooth transition of microwave lensing frequency shifts to the photon recoil shift for large wave packets.