We analyze the dynamical response of a two-dimensional system of itinerant fermions coupled to a scalar boson φ, which undergoes a continuous transition towards nematic order with a d-wave form factor. We consider two cases: (a) when φ is a soft collective mode of fermions near a Pomeranchuk instability, and (b) when it is an independent critical degree of freedom, such as a composite spin order parameter. In both cases, the order parameter is not a conserved quantity and the d-wave fermionic polarization Π(q,Ω) remains finite even at q=0. The polarization Π(0,Ω) has similar behavior in the two cases, but the relations between Π(0,Ω) and the bosonic susceptibility χ(0,Ω) are different, leading to different forms of χ′′(0,Ω), as measured by Raman scattering. We compare our results with polarization-resolved Raman data for the Fe-based superconductors FeSe1-xSx,NaFe1-xCoxAs, and BaFe2As2. © 2018 American Physical Society.