We study numerically a spherical particle settling through a density transition layer at moderate Reynolds numbers Re_{u}=69∼259 for the upper fluid. We investigate how the transition layer thickness affects the particle's bouncing behavior as it crosses the interface. The previous intuitive understanding was that the bounce occurs when the relative thickness of the transition layer, L/D, which is characterized by the ratio of the layer thickness L to the particle diameter D, is small. Indeed, we report no bounce phenomenon for very thick interfaces, i.e., L/D>10 in the current parametric range. However, we argue that the bounce can also be inhibited when L/D is too small. Upon a fixed upper layer Reynolds number Re_{u}=207 with varying L/D, we examine the flow evolution of these cases. We propose that this inhibition is attributed to two mechanisms. First, as the interface thickness decreases, the detachment of the attached lighter fluid from the upper layer occurs more rapidly, resulting in a faster decrease in buoyancy. Second, in the case of a very thin interface (L/D=0.5-3.0), the residual light fluid accumulates and undergoes a secondary detachment, separating from the particle at an angle relative to the central axis. This secondary detachment reduces the drag force and effectively prevents the particle from experiencing a rebound motion.