Air-sea turbulent heat fluxes play a fundamental role in generating and dampening sea surface temperature (SST) anomalies. To date, the turbulent heat flux feedback (THFF) is well quantified at basin-wide scales (~20 W~m^{-2}~K^{-1}) but remains unknown at the oceanic mesoscale (10-100 km). Here, using an eddy-tracking algorithm in three configurations of the coupled climate model HadGEM3-GC3.1, the THFF over mesoscale eddies is estimated. The THFF magnitude is strongly dependent on the ocean-to-atmosphere regridding of SST, a common practice in coupled models for calculating air-sea heat flux. Our best estimate shows that the mesoscale THFF ranges between 35 and 45 W~m^{-2}~K^{-1} globally, across different eddy amplitudes. Increasing the ratio of atmosphere-to-ocean grid resolution can lead to an underestimation of the THFF, by as much as 75% for a 6:1 resolution ratio. Our results suggest that a large atmosphere-to-ocean grid ratio can result in an artificially weak dampening of mesoscale SST anomalies.