We report our investigation on the electron-phonon coupling in graphite using scanning tunneling microscopy/spectroscopy (STM/STS), in combination with angle-resolved photoemission spectroscopy (ARPES). The exhibition of a gaplike feature near the Fermi level both in the STS and ARPES spectra confirms its intrinsic origination because of the electron-phonon coupling in graphite, where the phonon modes at $\ifmmode\pm\else\textpm\fi{}65$ and $\ifmmode\pm\else\textpm\fi{}160$ meV are highly resolvable in the clean samples. Under our controlled experiment using W, Pt/Ir, and Ag tips, we find that the presence of hydrogen at the tip apex or in the tip-substrate gap is responsible for smearing out the gaps in the STS spectra by providing additional tunneling channels. Due to its small adsorption energy of hydrogen for Ag among these tip materials, our results suggest that the use of Ag tips can be more suitable for resolving the intrinsic phonon-induced property in carbon-based materials.