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Despite a growing number of observations of whistler waves in/around the reconnection diffusion region, the origin of the whistler waves in the diffusion region and their role in reconnection remain elusive. This paper investigates the whistler-mode waves within an electron-scale reconnecting current sheet observed by the Magnetospheric Multiscale mission on 23 December 2016. These whistlers were observed in both the electron diffusion region (EDR) and the immediate inflow region of the electron-scale magnetic reconnection site. The dispersion relation of these whistlers is measured and compared to predictions from linear theory for the first time in these regions. The comparison shows that the field-aligned drifting electron component critically modifies the dispersion relation of whistlers in the EDR due to the Doppler-shift effects. We demonstrate that these whistlers propagated into the EDR from outside rather than locally excited, however, they did not provide sufficiently large anomalous dissipation in this EDR.