Kalb-Ramond (KR) gravity is an intriguing model incorporating local Lorentz violation, and black hole (BH) solutions are known to exist. In this study, we investigate some crucial aspects of BHs endowed with a global monopole charge in the self-interacting KR field. Specifically, we study the quasinormal modes (QNMs) corresponding to scalar, electromagnetic, and gravitational perturbations; derive rigorous bounds for the greybody factors (GBFs); and examine the sparsity of Hawking radiation. The effects of the model parameters ℓ (Lorentz-violating parameter in KR gravity) and η (monopole charge) on these phenomena are elaborated. First, QNMs are evaluated with high precision using the 13 ^th -order Padé-averaged WKB method and cross-examined via time-domain analyses within an acceptable parameter space. The results show that the estimated QNMs are more sensitive to ℓ; however, both model parameters influence the frequency spectra. The derived bounds on the GBFs aid in further constraining the parameter space. It is shown that ℓ and η have a similar effect on the greybody bounds. Furthermore, positive and negative values of ℓ have opposing effects in that the bounds are reversed for the two cases. The analyses of the Hawking radiation sparsity highlight the effect of ℓ, and two scenarios are noted: either the radiation emitted is less sparse than Hawking radiation, or it is sparser during the evaporation phase. Thus, this work presents a comprehensive account of BHs in KR gravity with a global monopole charge.