Excitons in semiconductors and molecules are widely utilized in photovoltaics and optoelectronics, and high-temperature coherent quantum states of excitons can be realized in artificial electron-hole bilayers and an exotic material of an excitonic insulator (EI). Here, we investigate the band gap evolution of a putative high-temperature EI Ta₂NiSe₅ upon surface doing by alkali adsorbates with angle-resolved photoemission and density functional theory (DFT) calculations. The conduction band of Ta₂NiSe₅ is filled by the charge transfer from alkali adsorbates, and the band gap decreases drastically upon the increase of metallic electron density. Our DFT calculation, however, reveals that there exist both structural and excitonic contributions to the band gap tuned. While electron doping reduces the band gap substantially, it alone is not enough to close the band gap. In contrast, the structural distortion induced by the alkali adsorbate plays a critical role in the gap closure. This work indicates a combined electronic and structural nature for the EI phase of the present system and the complexity of surface doping beyond charge transfer.