Ionospheric scintillation can affect not only satellite communications but also satellite measurements of the ionosphere, such as the measurements of total electron content (TEC) made using Transit-like signal transmissions. In this work a numerical phase-screen propagation simulation is applied to study the accuracy of the measurement of TEC made with Transit-like signals. To measure TEC, the phase from coherently related 150 and 400 MHz tones is combined to obtain an estimate of the phase imparted to a propagating signal by transmission through the ionosphere. This phase is processed to remove ambiguities of 2π and converted to a relative value of TEC. However, scattering caused by ionospheric irregularities produces amplitude fading and phase variations that degrade the TEC measurement in several ways. Rapid phase variations that may be associated with deep fades can degrade the phase-ambiguity removal process. Fresnel filtering causes scintillation when intrinsic ionospheric variations are of the size of the Fresnel zone and smaller. Receiver noise also acts to degrade the phase measurements and is especially important during the deepest fades. This paper considers the effects of all these processes and develops rule-of-thumb qualifiers to assure the accuracy of Transit-like measurements of TEC.