Fast electrons created as a result of the laser beam interaction with a solid target penetrate into the target material and initialize processes leading to the generation of the characteristic X-ray K-α radiation. Due to the strong electric field induced at the rear side of a thin target the transmitted electrons are redirected back into the target. These refluxing electrons increase the K-α radiation yield, as well as the duration of the X-ray pulse and the size of the radiation emitting area. A model describing the electron refluxing was verified via particle-in-cell simulations for non-relativistic electron energies. Using this model it was confirmed that the effect of the electron refluxing on the generated X-ray radiation depends on the target thickness and the target material. A considarable increase of the number of the emitted K-α photons is observed especially for thin targets made of low-Z materials, and for higher hot electron temperatures.