Mesoscale eddies, generated by lateral gradients in salinity and temperature in the Arctic marginal ice zone, are known to modulate the melting of sea ice. Yet, it remains unclear if eddies modify sea ice growth during the freezing season. Here, we use idealized spin-down simulations of a front to explore the sea ice growth above an eddying ocean. In the presence of eddies, mixing of the sea surface temperature and salinity induces spatial variability in the heat and salt fluxes at the ice-ocean interface, imprinting spatial variability on the sea ice thickness. Sea ice thickness shows an order of magnitude more spatial variability in our simulations with strong eddies compared to those without. Increased spatial heterogeneity in the sea ice could make it more brittle and affect its evolution. This effect may become more pronounced as the Arctic transitions to a summer open-ocean regime and the eddy field intensifies.