We consider a quantum dot (QD) embedded in one arm of an electronic Mach-Zehnder interferometer (MZI). We address the transmission phase through the QD (evidently, in the presence of a strong magnetic field), and study the conditions under which transmission phase lapses occur. It turns out that the physics is substantially different from that of the transmission phase through a QD in the absence of a magnetic field. Specifically, certain degrees-of-freedom of the QD act as a detector (in essence a dephasor) to the coherent transport through the respective arm of the MZI. Additionally, we study the coherency of the system (MZI), which is affected by non-Gaussian fluctuations in the detector (QD). The relation between dephasing in the MZI and the Friedel sum rule will be pointed out. Recent experimental results will be briefly discussed.