Nick-sensing 3'-phosphoesterase involved in a base excision repair pathway required for active DNA demethylation. The N-terminal DNA-binding domain binds specifically to gap sites and sharply bends the target DNA. Lacks 5'-kinase activity but is capable of 3'-phosphoglycolate end processing. Inactive on 3'-alpha,beta-unsaturated aldehyde (3'-dRP). Protects partially genes from transcriptional silencing by preventing promoter DNA hypermethylation. a 3'end (2'-deoxyribonucleotide 3'-phosphate)-DNA + H2O = a 3'-end 2'-deoxyribonucleotide-DNA + phosphate Activated by the presence of DNA (PubMed:11948185). Stimulated by XRCC1 (PubMed:23316050). Interacts with ROS1 (via the central region) (PubMed:22325353). Binds to XRCC1 (PubMed:23316050). Not found in the nucleolus (PubMed:22325353). Co-localizes in nucleoplasmic foci with APE1L and ROS1, two components of the DNA demethylase machinery (PubMed:25569774). No visible phenotype under normal growth conditions (PubMed:22325353, PubMed:25569774). Loss of 3'-phosphatase activity and hypersensitivity to DNA-damaging agents (PubMed:22325353). Increased DNA methylation and transcriptional gene silencing (PubMed:22325353). Zdp ape1l double mutants are embryo lethal and cause DNA hypermethylation and down-regulation of imprinted genes in the endosperm (PubMed:25569774). In the C-terminal section; belongs to the DNA 3' phosphatase family.