Sea ice modulates the energy exchange between the atmosphere and the ocean through its kinematics. Marginal ice zone (MIZ) dynamics are complex and are not well resolved in routine observations. Here, we investigate sea ice dynamics in the Greenland Sea MIZ using two Lagrangian drift datasets. We find evidence of tidal currents strongly affecting sub-daily sea ice motion. Velocity anomalies show abrupt transitions aligned with gradients in seafloor topography, indicating changes in ocean currents. Remote-sensed ice floe trajectories derived from moderate resolution satellite imagery provide a view of small-scale variability across the Greenland continental shelf. Ice floe trajectories reveal an west-east increasing velocity gradient imposed by the East Greenland Current, with maximum velocities aligned along the continental shelf edge. These results highlight the importance of small scale ocean variability for ice dynamics in the MIZ.