In this work, electron impact ionizing collisions on atomic hydrogen embedded in weakly coupled plasmas are studied at impact energies of 80 and 150 eV. Fully differential cross sections calculated by means of a distorted wave model which explicitly considers the screening effect among the three interacting particles in the final state are presented and analyzed. Compared to the unscreened case, clear differences in shape and magnitude are found for the dominant structures, the binary and recoil peaks, suggesting that the role played in the collision by the different particles varies with the Debye screening length. A scaling law for the fully differential cross section in terms of the nuclear charge Z, first proposed by Kornberg and Miraglia in the photo-double ionization context, is shown to also hold for the electron impact ionization of hydrogenic ions in the present screened context.