  The stability of Reissner-N\"ordstrom black holes with an extremal
mass-charge relation was determined by calculating the propagation speed of
gravitational waves on this background in an effective field theory (EFT) of
gravity. New results for metric components are shown, along with the
corresponding new extremal relation, part of which differs by a global factor
of 2 from the past published work. This new relation further develops the
existing constraints on EFT parameters. The radial propagation speed for
gravitational waves in the Regge-Wheeler gauge was calculated linearly for all
perturbations, yielding exact luminality for all dimension-4 operators. The
dimension-6 radial speed modifications introduce no constraints on the sign of
the modified theory parameters from causality arguments, while the deviation
from classical theories vanishes at both horizons. The angular speed was found
to be altered for the dimension-4 operators, with possible new constraints on
the modified theory being suggested from causality arguments. Results are
consistent existing literature on Schwarzschild black hole backgrounds, with
some EFT terms becoming active only in non-vacuum spacetimes such as
Reissner-N\"ordstrom black holes.
