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We present a new analysis of the James Webb Space Telescope infrared (IR) spectra of GRB 230307A(AT 2023vfi), a long gamma-ray burst (GRB) with an IR excess and spectral lines suggestive of significant heavy r-process production. The spectra, taken 29 and 61 d after the GRB trigger, have blackbody-like continua with <inline-formula><tex-math>$T_{\rm eff} \approx 550$</tex-math></inline-formula> K and an emission line near 2.1 μm, previously attributed to [Te 3]. This line identification has been used as evidence for an r-process-powered kilonova (KN), despite no KN model producing a blackbody-like spectrum at late times. Such an IR continuum could be emitted by newly formed dust, and we model the thermal emission to infer dust properties, including composition and mass. We find that the emission requires at least 3─<inline-formula><tex-math>$6 \times 10^{-3}$</tex-math></inline-formula> M<inline-formula><tex-math>$_{\odot }$</tex-math></inline-formula> of carbon or silicate dust, which is inconsistent with r-process yields expected from a neutron-star merger. Alternatively, the continuum could be from <inline-formula><tex-math>$2\times 10^{-3}$</tex-math></inline-formula> M<inline-formula><tex-math>$_{\odot }$</tex-math></inline-formula> of metallic iron dust, which is mildly consistent (at 3<inline-formula><tex-math>$\sigma$</tex-math></inline-formula>) with KN models, but such dust is unlikely to form in the expanding ejecta. GRB 230307A's low late-time luminosity also constrains the amount of radioactive <inline-formula><tex-math>$^{56}$</tex-math></inline-formula>Ni produced to &lt;<inline-formula><tex-math>$6.3 \times 10^{-2}$</tex-math></inline-formula> M<inline-formula><tex-math>$_{\odot }$</tex-math></inline-formula> (3<inline-formula><tex-math>$\sigma$</tex-math></inline-formula>). No KN model can simultaneously form the necessary dust for the IR continuum and heavy elements for the [Te 3] line. We conclude that the blackbody continuum is not due to dust emission, or GRB 230307A did not originate from a binary compact-object merger.