With the simultaneous increase in the number of endoprostheses being performed, advances in the field of biomaterials are becoming apparent—whereby the materials and technologies used to construct implants clearly improve the implants’ quality and, ultimately, the life of the patient after surgery. The aim of this study was to modify the titanium alloy Ti6Al4V ELI used in the construction of hip joint endoprostheses. This is why the continuous development of biomaterials is so important. This paper presents the results of research for a new application of polymer poly(ethylene-alt-maleic anhydride) as a drug release layer, placed on the surface of a titanium alloy. The obtained layers were analyzed using Raman spectroscopy (spectra and maps), Fourier transform infrared spectroscopy (spectra and maps), contact angle measurements as well as scanning electron microscopy and energy dispersive spectroscopy imaging and topography analysis. The results confirmed that the polymer layer obtained on the plate surface after the alkali heat treatment process is much better—it binds much more polymer and thus the applied drug. In addition, a longer and more gradual release of the drug was observed for the alkali heat treatment modification than for H2O2 solution.