Trapping electron-assisted magnetic recording (TEAMR) has been recently proposed as a method of lowering the magnetic anisotropy of magnetic data storage media during write cycles. In this paper, we studied theoretically the TEAMR feasibility when an additional dielectric nano-underlayer is incorporated within the recording medium. We report a comparative study between a standard TEAMR data storage system and a dielectric underlayer TEAMR system. Our results indicate a substantial improvement in the electron trapping mechanism when a dielectric underlayer is used. A direct consequence of the proposed system is the effective reduction of the local magnetic coercive field when using this modified TEAMR design, which opens up the possibility of future developments based on TEAMR technology.