Hard X-rays produced by the interaction of ps lasers with metal microwire can be used as micro- focus Compton backlighters, which is an important diagnostic tool in inertial confinement fusion research. In actual experiments, CH plastic foil is often used as a low-Z substrate to support the microwire. Based on the experimental results of laser-driven microwire micro-focus x-ray source carried out on the Xingguang III laser facility, We explored the influence of low-Z substrate and laser intensity on the energy conversion efficiency from laser to the bremsstrahlung x-rays. Through two- and three-dimensional particle-in-cell coupled with Monte Carlo simulations, as well as a semi-analytical model for the bremsstrahlung photon energy conversion efficiency, a reasonable physical explanation for the experimental results is given from the perspective of the electron refluxing effect. According to the model, the energy conversion efficiency of bremsstrahlung radiation is proportional to the number of refluxing electrons and the number of times they cross the solid target. It is shown that the low-Z substrate can effectively increase the energy deposition of the laser in the target, but decrease the laser-to-bremsstrahlung energy conversion efficiency, which can be reduced by decreasing the thickness of the substrate. It is also found that the photon energy conversion efficiency increases with the laser intensity.