This paper investigates the shadow and greybody bounding characteristics of a regular black hole in four-dimensional spacetime under scale-dependent gravity. The study focuses on determining constraints on the parameter $\tilde{\epsilon}$, which describes the scale-dependent solution relative to the observed shadow radius $R_{sh}$ from the Event Horizon Telescope (EHT) data for Sgr. A* and M87*. The results show that there is a unique value for $\tilde{\epsilon}$ corresponding to the mean of $R_{sh}$, with uncertainties possibly arising from fluctuations in the scale-dependent parameter. The parameter $\tilde{\epsilon}$ is positive for Sgr. A* and negative for M87*. Using M87* as a reference, the study examines the shadow radius and weak deflection angle under the given constraints. Discrepancies are observed in both the shadow and deflection angle of photons, particularly when the photon's impact parameter approaches the critical value. The paper also explores the greybody factor, which quantifies the probability of a particle or wave being absorbed or scattered by a black hole. The greybody factor depends on the energy and angular momentum of the incident particle or wave, as well as the black hole's properties. The study calculates the greybody bounding for the regular black hole solution, revealing insights into the interactions between matter and radiation near black holes. The results are presented in figures, showing how the shadow radius and weak deflection angle vary with the scale-dependent parameter $\tilde{\epsilon}$. The analysis highlights the importance of scale-dependent gravity in understanding black hole physics and its implications for quantum gravity. The study concludes that the scale-dependent parameter $\tilde{\epsilon}$ influences the black hole's shadow and greybody factor, providing a framework for further exploration of black hole properties in the context of scale-dependent gravity.This paper investigates the shadow and greybody bounding characteristics of a regular black hole in four-dimensional spacetime under scale-dependent gravity. The study focuses on determining constraints on the parameter $\tilde{\epsilon}$, which describes the scale-dependent solution relative to the observed shadow radius $R_{sh}$ from the Event Horizon Telescope (EHT) data for Sgr. A* and M87*. The results show that there is a unique value for $\tilde{\epsilon}$ corresponding to the mean of $R_{sh}$, with uncertainties possibly arising from fluctuations in the scale-dependent parameter. The parameter $\tilde{\epsilon}$ is positive for Sgr. A* and negative for M87*. Using M87* as a reference, the study examines the shadow radius and weak deflection angle under the given constraints. Discrepancies are observed in both the shadow and deflection angle of photons, particularly when the photon's impact parameter approaches the critical value. The paper also explores the greybody factor, which quantifies the probability of a particle or wave being absorbed or scattered by a black hole. The greybody factor depends on the energy and angular momentum of the incident particle or wave, as well as the black hole's properties. The study calculates the greybody bounding for the regular black hole solution, revealing insights into the interactions between matter and radiation near black holes. The results are presented in figures, showing how the shadow radius and weak deflection angle vary with the scale-dependent parameter $\tilde{\epsilon}$. The analysis highlights the importance of scale-dependent gravity in understanding black hole physics and its implications for quantum gravity. The study concludes that the scale-dependent parameter $\tilde{\epsilon}$ influences the black hole's shadow and greybody factor, providing a framework for further exploration of black hole properties in the context of scale-dependent gravity.