  AX J1745.6-2901 is an eclipsing low mass X-ray binary (LMXB) in the Galactic
Centre (GC). It shows significant X-ray excess emission during the eclipse
phase, and its eclipse light curve shows an asymmetric shape. We use archival
XMM-Newton and Chandra observations to study the origin of these peculiar X-ray
eclipsing phenomena. We find that the shape of the observed X-ray eclipse light
curves depends on both photon energy and the shape of the source extraction
region, and also shows differences between the two instruments. By performing
detailed simulations for the time-dependent X-ray dust scattering halo, as well
as directly modelling the observed eclipse and non-eclipse halo profiles of AX
J1745.6-2901, we obtained solid evidence that its peculiar eclipse phenomena
are indeed caused by the X-ray dust scattering in multiple foreground dust
layers along the line-of-sight (LOS). The apparent dependence on the
instruments is caused by different instrumental point-spread-functions. Our
results can be used to assess the influence of dust scattering in other
eclipsing X-ray sources, and raise the importance of considering the timing
effects of dust scattering halo when studying the variability of other X-ray
sources in the GC, such as Sgr A*. Moreover, our study of halo eclipse
reinforces the existence of a dust layer local to AX J1745.6-2901 as reported
by Jin et al. (2017), as well as identifying another dust layer within a few
hundred parsecs to Earth, containing up to several tens of percent LOS dust,
which is likely to be associated with the molecular clouds in the Solar
neighbourhood. The remaining LOS dust is likely to be associated with the
molecular clouds located in the Galactic disk in-between.
