The production of water masses formed by convection in the Labrador Sea (i.e. Labrador Sea Water, LSW) and its variability contributes to the variability of the Atlantic Meridional Overturning Circulation (AMOC). Several studies put the role of the Labrador Sea under renewed debate, and suggest a rather complex interplay between the production of the LSW, the boundary current and the eddy field. To this end, an increased effort is put in understanding the variability of the LSW, its export routes and associated export timescales. In this study, the effects of variations in boundary current strength on the export pathways of convected water masses are investigated. The same idealized eddy-resolving numerical model is used as Georgiou et al. (2019) which has proven to be capable of capturing the key dynamics of the Labrador Sea, like the annual cycle of convection, the process and timescales of restratification, and properties of the mesoscale eddy field. Model simulations are set-up with different scenarios of the density structure of the boundary current at inflow location (i.e. southern tip of Greenland). The variations result in respectively a 5% strengthening and 5% weakening of the boundary current, which corresponds to interannual variability of observed surface velocities. The model output demonstrates that boundary current variations start a chain of reactions, significantly changing the dynamics of the Labrador Sea. This has implications for deep convection processes in the interior of the basin and thus the export product. With a passive tracer analysis it is shown that convected water masses formed in the convection area are laterally steered along isopycnals by an eddy-induced shear flow from the interior towards the boundary current at the West-Greenland coast in deeper layers. A strengthening (weakening) of the boundary current yields a lighter (denser) water mass to be exported at shallower (deeper) layers out of the interior. The most intense entrainment into the boundary current occurs where both the density and depth of the convected water masses match the local water mass properties of the boundary current, and where eddies detach from the boundary current. The associated export timescales can be linked to the location where eddies detach, and to the strength of the eddy-induced shear flow. This study further highlights the implications for linking variability in the LSW production and export to AMOC variability as the total export of convected waters in the Labrador Sea is a mixture of multiyear convected waters. Based on density alone, measurements of water masses at the exit do not directly reveal the past-year dynamical state of the Labrador Sea. This emphasizes that a proper representation of mesoscale eddies in models is necessary for representing the export timescales and water mass properties of the LSW, and their response to changing forcing.