Telomeres protect chromosome ends from unscheduled DNA repair. Of particular concern to telomere integrity is the action of the MRN (MRE11, RAD50, NBS1) complex, which plays a critical role in the recognition and processing of double-stranded DNA breaks (DSBs). MRN orchestrates activation of the ATM kinase in the cellular response to DNA damage, promotes DNA end-tethering thus aiding the nonhomologous end joining (NHEJ) pathway, and initiates DSB resection through the nuclease activity of MRE11. A previously identified amino acid motif (which we refer to as MIN, for MRN inhibitor) is capable of regulating MRN activity via binding to a RAD50 interface. The motif has independently arisen at least twice in yeasts, through convergent evolution of telomeric proteins Rif2 and Taz1, in budding and fission yeast respectively. We now provide a third example of convergent evolution for this mechanism controlling the activity of MRN at telomeres, by demonstrating that the iDDR motif of shelterin protein TRF2 binds to RAD50 at the same site engaged by the MIN motif in the yeast proteins, despite not sharing any sequence conservation with the latter. Modelling for the human CtIP interaction with RAD50 (known to be necessary for activation of MRE11), as well as for the budding and fission yeast counterparts Sae2 and Ctp1, indicates that the interaction is mutually exclusive with binding of the iDDR/MIN motifs, thus pointing to a clear conserved mechanism for inhibition of MRN nuclease activity at telomeres.