ABSTRACT The presence of low-amplitude peaks over the noise in the power spectra of $\delta$ Scuti stars is frequently disregarded. These seemingly insignificant peaks, collectively referred to as grass, might contain valuable information about the origin of these stars and the reasons behind the occurrence or absence of a plateau. It is crucial to systematically parametrize the grass phenomenon throughout a comprehensive sample that covers the entire $\delta$ Scuti star parameter range. Thus, we conduct a quantitative study of long-duration, high-duty-cycle Transiting Exoplanet Survey Satellite light curves, leading to improved detection methods for plateaus and a deeper understanding of their nature. This approach minimizes the impact of unresolved peaks caused by mode variations over time. Additionally, we present appropriate analysis techniques to mitigate window effects and identify and eliminate spurious peaks. We demonstrate here that the grass can be effectively parametrized based on peak density. With such parametrization two distinct regimes are found: the sparse grass regime, characterized by low peak density and the absence of a plateau in the power spectra, and the dense grass regime, characterized by high peak densities and the presence of an observable plateau. Our study is the first rigorous quantification of the emergence of such a plateau in the power spectra of $\delta$ Scuti stars. Since the grass might be related with fractality, mode variability, and stellar rotation rate, its parametrization opens a new way to analyse these stars.