Focused electron-beam-induced deposition (FEBID) is a promising nanolithography technique using "direct-write" patterning by carbon line and dot deposits on graphene. Understanding interactions between deposited carbon molecules and graphene enables highly localized modification of graphene properties, which is foundational to the FEBID utility as a nanopatterning tool. In this study, we demonstrate a unique possibility to induce dramatically different adsorption states of FEBID-produced carbon deposits on graphene, through density functional theory calculations and complementary Raman experiments. Specifically, an amorphous carbon deposit formed by direct irradiation of high energy primary electrons exhibits unusually strong interactions with graphene via covalent bonding, whereas the FEBID carbon formed due to low-energy secondary electrons is only weakly interacting with graphene via physisorption. These observations not only are of fundamental importance to basic physical chemistry of FEBID carbon-graphene interactions but also enable the use of selective laser-assisted postdeposition ablation to effectively remove the parasitically deposited, physisorbed carbon films for improving FEBID patterning resolution.