Radiation Backreaction in Relational GFT Cosmology: Homogeneous Newton Calibration and the Missing Finite-k Response Vertex

A published five-scalar relational group field theory (GFT) host contains a late-GR homogeneous fifth-matter branch whose Newton normalization is fixed by the host's GR matching/calibration, while independently reconstructing an inhomogeneous matter sector with relativistic finite-momentum propagation. This paper asks whether those lower-order properties are sufficient to derive the gravitational backreaction of a massless radiation state. At the level of the published source, they are not. The direct second-order free-host Madelung/amplitude channel has a source-exact leading-WKB obstruction. In the decoupled late-GR regime its quadratic phase source is Lagrangian/trace-like: relativistic on-shell massless WKB propagation cancels the leading O(omega^2 |q|^2) contribution, while the corresponding GR harmonic-time volume equation is sourced by 3 rho - p and is nonzero for radiation. The surviving corrections are adiabatically or late-time suppressed. Independently, the published coherent mean field and linear wave operator do not determine thermal state covariance, and the homogeneous Newton calibration fixes only the zero-momentum response leg R(0)=1, not a finite-k form factor R(k). The free-state channel is more subtle. For a positive free-state contribution expressible as a Laplace superposition V_grow(chi)=int exp(2 omega chi) dmu(omega), finite exponential moments at every finite chi exclude the finite harmonic-clock horizon required by an asymptotically dominant positive constant-w<1 GR component. Conversely, a tail dmu ~ omega^p exp(-2 omega chi_*) d omega gives V ~ (chi_* - chi)^(-(p+1)) and w=(p-1)/(p+1), so p=2 can reproduce the radiation clock law. Thus quadraticity alone does not exclude every state-dressed free geometric readout; such a channel requires additional state support with a finite Laplace abscissa and is not fixed by the published sharply peaked host state. The paper also proves a response-identifiability result and a preventive Hartree-class statement: within a declared circular-Gaussian, derivative-free local polynomial Hartree closure, all state dependence collapses to an equal-point covariance, whereas radiation energy is derivative weighted. Increasing polynomial order therefore does not generate the missing spectral information. The minimal source-exact positive completion is identified as a finite-momentum geometry-matter-matter response vertex, or an equivalent stress Ward identity, Rg;II=delta^3 Gamma_eff/(delta q_g delta I delta I). Homogeneous GR matching is therefore a calibration condition rather than a derivation of finite-k radiation backreaction.