Investigated is the ringdown phase of black holes within a modified gravitational framework that includes a weak Finsler coupling (a) , a quadratic curvature correction (b) and a dynamical timelike vector field (u^μ). Using analytical approximations and dicussing numerical simulations, there is shown, that quasinormal modes (QNM) are slightly shifted and anisotropically modulated. Residuals against standard Kerr fits are calculated, and observational constraints from LIGO, Virgo, pulsar timing, and atomic clocks are analyzed. Found is, that current gravitationalwave detectors constrain (a≾10 −3 ), while next-generation detectors (Einstein Telescope, LISA) could probe (a∼10 −12 −10 −8 ). Quadratic curvature corrections remain unobservable at thePlanck scale. The given results highlight characteristic signatures of Finsler-modified gravity in black hole ringdowns.