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In type I seesaw models, the right-handed neutrinos are typicallysuper-heavy, consistent with the generation of baryon asymmetry via standardleptogenesis. Primordial gravitational waves of cosmological origin provides anew window to probe such high scale physics, which would otherwise beinaccessible. By considering a {\em global} $U(1)_{B-L}$ extension of the typeI seesaw model, we explore the connection between the heaviest right-handedneutrino mass and primordial gravitational waves arising from the dynamics ofglobal cosmic string network. As a concrete example, we study a global$U(1)_{B-L}$ extension of the Littlest Seesaw model, and show that theinevitable GW signals, if detectable, probe the parameter space that canaccommodate neutrino oscillation data and successful leptogenesis, whilerespecting theoretical constraints like perturbativity of the theory. IncludingCMB constraints from polarization and dark radiation leaves a large region ofparameter space of the model, including the best fit regions, which can beprobed by GW detectors like LISA and ET in the near future. In general, the GWdetectors can test high scale type I seesaw models with the heaviestright-handed neutrino mass above $2.5 \times 10^{14}$ GeV, assuming theperturbativity, and $7 \times 10^{13}$ GeV assuming that the coupling betweenthe heaviest right-handed neutrino and the $U(1)_{B-L}$ breaking scalar is lessthan unity.

Cosmic string gravitational waves from global $U(1)_{B-L}$ symmetry breaking as a probe of the type I seesaw scale