Oxidative intrastrand cross-links where two nucleobases are covalently tethered form a particularly harmful class of DNA lesions. Their formation follows a radical pathway, as initiated by reactive oxygen species, which often ends with the departure of the hydrogen H8 of guanine to restore a closed-shell adduct. The ease of this abstraction step is investigated here for three systems of increasing complexity, C8-methyleguanine, the guanine-thymine dinucleoside monophosphate (GpT), and GpT embedded in a hexameric DNA sequence. First-principle calculations, combined with semiempirical approaches for the latter system, are performed to determine the energetics of the intermediates and to compare their respective exergonicities, which turned out to significantly depend on the environment. The hydrogen departure path is shown to be strongly favored compared to usual H-abstraction sites for normal guanine, while the impact of the biological environment is evidenced as the H8 departure becomes more difficult when larger structures are considered. A computational assessment of a plausible oxime intermediate is discussed as well.