Quadratic (free-fermion) Hamiltonians on a lattice provide an exactly solvable platform for open-system dynamics, while quantum Zeno and anti-Zeno effects show how finite-time interventions can suppress or enhance decay in a way controlled by the environment spectrum. Here we study local fermionic excitations coupled to a tight-binding band and subjected to stroboscopic system re-preparation with interval $\tau$. In the weak-coupling regime, we derive the one-interval survival probability and the associated finite-interval loss rate as a universal spectral-filter functional of the bath spectral density. We distinguish explicitly between unconditional re-preparation, for which the physically nontrivial observable is the loss accumulated between re-preparations, and a repeated projective-survival protocol, for which the same rate controls the multi-cycle survival probability to leading order in the coupling. The rate interpolates between short-time Zeno suppression and the long-time golden-rule limit. We then specialize to a fermionic tight-binding ring and obtain the exact band spectral density for a locally coupled mode. Finally, for a two-site system coupled through spatially separated contacts, interference generates structured symmetric and antisymmetric spectral densities with interior dark energies; finite-$\tau$ spectral broadening can activate decay near such golden-rule dark points and enables mode-selective control.