The chiral anomaly is a characteristic phenomenon of Weyl fermions, which has condensed matter realizations in Weyl semimetals. Efforts to observe smoking gun signatures of the chiral anomaly in Weyl semimetals have mostly focused on a negative longitudinal magnetoresistance in electronic transport. Unfortunately, disentangling the chiral anomaly contribution in transport or optical measurements has proven nontrivial. Recent works have proposed an alternative approach of probing pseudoscalar phonon dynamics for signatures of the chiral anomaly in non-mirror-symmetric crystals. Here we show that such phonon signatures can be extended to scalar phonon modes and mirror-symmetric crystals, broadening the pool of candidate materials. We show that the presence of the background magnetic field can break mirror symmetry strongly enough to yield observable signatures of the chiral anomaly. Specifically for mirror-symmetric Weyl semimetals such as TaAs and NbAs, including the Zeeman interaction at |B|≈10 T, we predict that an IR reflectivity peak will develop with an EIR·B dependence.