Genetic analyses indicate minimal gene flow across the so-called Eastern Pacific Barrier (EPB) in larvae of the reef-building coral \emph{Porites lobata}. Notably, Clipperton Atoll, situated on the eastern side of the EPB, is the only site that exhibits detectable genetic connectivity with the Line Islands, which lie to the west of the EPB. To elucidate the relationship between this genetic signal and large-scale Pacific Ocean circulation, we analyze historical trajectories of surface-drifting buoys from the Global Drifter Program (GDP). We first discretize the GDP drifter trajectories into a Markov chain representation and subsequently apply transition path theory (TPT) in combination with Bayesian inference. The TPT analysis identifies reactive trajectories -- pathways that connect the Line Islands to Clipperton Atoll with minimal detours -- whose travel times do not exceed 5 months, which is taken as an upper bound for the larval survival time of \emph{P. lobata}. Consistently, the posterior distribution of transport from Pacific islands west of the EPB to Clipperton Atoll attains a local maximum in the Line Islands at a travel time of approximately 2.5 months. Our probabilistic characterization of the Lagrangian dynamics therefore supports a scenario of weak, but non-negligible, permeability of the EPB, in agreement with the genetic evidence, and it motivates a refined dynamical definition of the EPB based on the remaining duration of reactive trajectories. Furthermore, our results indicate that the connectivity between the Line Islands and Clipperton Atoll is governed primarily by the seasonal modulation of the North Equatorial Countercurrent, rather than by the phase of the El Niño--Southern Oscillation (ENSO). Finally, Clipperton Atoll's role as a terminal sink for trajectories is relevant to the planned mining operations.