Beam scanning is a fundamental requisite for mobile ground terminals of satellite communication systems. Mechanical steering using transmit-arrays (TAs) has been studied as a cost-effective alternative to phased array antennas. The design of the primary feed for this type of aperture can be challenging in the context of satellite-on-the-move (SOTM) applications. Several antenna specifications must be implemented at feed level, including dual-band operation with switchable orthogonal circular polarization states for multi-spot satellite handover. A new modular design approach for the feed system of TA antennas is presented comprising: i) a low gain dual-port linearly polarized waveguide antenna for polarization switching; ii) a dual-band polarizer for orthogonal Rx/Tx circular polarizations conversion; iii) a dielectric lens for a proper illumination taper of the TA, which creates a virtual focus in both bands behind the feed structure. This approach allows the feed integration with the dual-band TA, without increasing the overall height of the terminal relative to the TA focal length. The concept is validated experimentally in a complete antenna system with dimensions of 196 x 147 mm2, which provides mechanical scanning up to 50º from boresight with 23 dBi and 25 dBi of gain at 20 GHz and 30 GHz, respectively.