We investigate the influence of launching conditions on misalignment tolerance of pluggable ballpoint-pen interconnects, where graded-index plastic optical fibers (GI POFs) are coupled with ball lenses mounted on their end faces. The lateral-misalignment tolerance of the ballpoint-pen connector decreased with an increase in the driving current of a vertical cavity surface emitting laser (VCSEL) under the center launching condition. This was attributed to the VCSEL multimode oscillation, which increased the connector coupling loss through the higher-order guided mode launching in the GI POF and the resulting output beam expansion in the ballpoint-pen connector. The driving-current dependence of the connector coupling loss could be decreased using offset launchings. For a radial launching offset of 20µm, we could obtain coupling losses below 1dB for lateral coupling offsets of ±50µm with little dependence on the driving current. This suggests that data transmission quality for misaligned connection of the GI POFs can be improved further by optimizing launching systems for the ballpoint-pen interconnects.