By using all atom molecular dynamics simulations, we studied the behavior of human DNA telomere sequences in guanine quadruplex (G4) conformation and in the presence of oxidative lesions, namely abasic sites. In particular, we evidenced that while removing one guanine base induces a significant alteration and destabilization of the involved leaflet, human telomere oligomers tend, in most cases, to maintain at least a partial quadruplex structure, eventually by replacing the empty site with undamaged guanines of different leaflets. This study shows that (i) the disruption of the quadruplex leaflets induces the release of at least one of the potassium cations embedded in the quadruplex channel and that (ii) the electrostatic interactions of the DNA sequence with the aforementioned cations are fundamental to the maintenance of the global quadruplex structure.