We demonstrate that changes in the incident radiation in Mg ii h and k lines have a significant impact on the results of radiative transfer modeling of prominence-like plasmas. To uncover the extent of this impact and allow easy comparison, here we study two cases, one representing the minimum of the solar activity and the other corresponding to the typical conditions during solar maxima. To represent well the properties of the prominence plasma, we use the 2D non-LTE (i.e., departures from local thermodynamic equilibrium) model of prominence fine structures in both the single-thread configuration and the multithread configuration incorporating prominence dynamics. We show that in the modeled environment of prominence fine structures, the change in the central, integrated, and peak intensities of the synthetic Mg ii h and k profiles can be as large as the change in the incident radiation itself. This means that the Mg ii h and k spectra of observed prominences can be affected by tens of percent because the illumination from the solar disk can change by such a degree over the solar cycle. That makes the knowledge and use of event-specific incident radiation data very important for the diagnostics of prominences and other chromospheric and coronal structures when using Mg ii h and k spectral observations. In addition, the observed Mg ii h and k spectra are strongly influenced by the line-of-sight dynamics, as the multithread configuration of the 2D model allows us to reveal. The effect of dynamics is, unsurprisingly, most pronounced in the line widths and integrated intensities.