Key regulator of TP53BP1 required to stabilize TP53BP1 and regulate its recruitment to chromatin. In absence of DNA damage, interacts with the tandem Tudor-like domain of TP53BP1, masking the region that binds histone H4 dimethylated at 'Lys-20' (H4K20me2), thereby preventing TP53BP1 recruitment to chromatin and maintaining TP53BP1 localization to the nucleus. Following DNA damage, ATM-induced phosphorylation of TP53BP1 and subsequent recruitment of RIF1 leads to dissociate NUDT16L1/TIRR from TP53BP1, unmasking the tandem Tudor-like domain and allowing recruitment of TP53BP1 to DNA double strand breaks (DSBs). Binds U8 snoRNA. Homodimer (PubMed:26100207). Interacts with TP53BP1 (via the Tudor-like domain); interaction is abolished following DNA damage and TP53BP1 phosphorylation by ATM (By similarity). Interacts (via the cytoplasmic part) with SDC4 (PubMed:11805099). Interacts with TGFB1I1 and PXN (PubMed:11805099). Belongs to the Nudix hydrolase family. TIRR subfamily. Although strongly related to the nudix NUDT16 protein, lacks the Nudix box and is therefore not related to the rest of the family. Lacks a number of residues which are necessary for hydrolase activity and does not play a role in U8 snoRNA decapping activity.