Earlier studies demonstrated that the monitoring of the ionospheric total electron content (TEC) by global satellite navigation systems is a powerful method to study the propagation of transient disturbances in the ionosphere, induced by internal gravity waves. This technique has turned out to be sensitive enough to detect ionospheric signatures of magnetohydrodynamic waves as well. However, the effect of TEC modulation by ULF waves is not well examined as a responsible mechanism has not been firmly identified. During periods with intense Pc5 waves distinct pulsations with the same periodicity were found in the TEC data from high-latitude GPS receivers in Scandinavia. We analyze jointly responses in TEC variations and EISCAT ionospheric parameters to global Pc5 pulsations during the recovery phase of the strong magnetic storms on October 31, 2003. Comparison of periodic fluctuations of the electron density at different altitudes from EISCAT data shows that main contribution into TEC pulsations is provided by the lower ionosphere, up to ~150 km, that is the E-layer and lower F-layer. This observational fact favors the TEC modulation mechanism by field-aligned plasma transport induced by Alfven wave. Analytical estimates and numerical modeling support the effectiveness of this mechanism. Though the proposed hypothesis is basically consistent with the analyzed event, the correspondence between magnetic and ionospheric oscillations is not always perfect, so further studies need to be conducted to understand fully the TEC modulations associated with Pc5 pulsations.