This is the pre-review draft of the second of two papers submitted to Journal of Lightwave Technology, where the effect on confinement loss of thickness variations along the perimeter of the tubes composing the cladding of inhibited-coupling guiding Tubular Lattice hollow-core fibers is investigated by using the Azimuthal Fourier Decomposition technique (developed in Part I) for the description of the cladding modal dynamics and their interaction with fundamental core mode. The results show that the thickness inhomogeneity affects the confinement loss spectrum through confinement loss increase and frequency red- and blue-shift of the high loss spectral regions. The magnitudes of the confinement loss increase and the high-loss region frequency shift strongly depend on the spatial distribution of the thickness inhomogeneity. The study provides insight into the loss mechanism of non-ideal tube lattice fibers, it allows quantifying the impact of such kind of structural deformations, identifying the route to make fibers more resilient to such fabrication imperfections, and highlighting once again the importance played in inhibited-coupling fibers by the interaction between core modes and the intricate set of cladding modes.