We predict that dynamical strain can induce a bulk orbital magnetization in time-reversal- (TR-) invariant Weyl semimetals (WSMs) that are gapped by charge-density waves (CDWs) -- a class of systems experimentally observed this past year. We term this effect the ``dynamical piezomagnetic effect" (DPME). By studying the low-energy effective theory and a minimal tight-binding (TB) model, we find that the DPME originates from an effective valley axion field that couples the electromagnetic gauge field with a strain-induced pseudo-gauge field. In particular, the DPME represents the first example of a fundamentally 3D strain effect originating from the Chern-Simons 3-form, in contrast to the previously-studied piezoelectric effects characterized by 2D Berry curvature. We further find that the DPME has a discontinuous change when the surface of the system undergoes a topological quantum phase transition (TQPT), and thus, that the DPME provides a bulk signature of a boundary TQPT in a TR-invariant Weyl-CDW.