We present a JWST/Near Infrared Camera (NIRCam) transmission spectrum from 3.9 to 5.0 μm of the recently validated sub-Earth GJ 341b (R P = 0.92 R ⊕, T eq = 540 K) orbiting a nearby bright M1 star (d = 10.4 pc, K mag = 5.6). We use three independent pipelines to reduce the data from the three JWST visits and perform several tests to check for the significance of an atmosphere. Overall, our analysis does not uncover evidence of an atmosphere. Our null hypothesis tests find that none of our pipelines’ transmission spectra can rule out a flat line, although there is weak evidence for a Gaussian feature in two spectra from different pipelines (at 2.3 and 2.9σ). However, the candidate features are seen at different wavelengths (4.3 μm versus 4.7 μm), and our retrieval analysis finds that different gas species can explain these features in the two reductions (CO2 at 3.1σ compared to O3 at 2.9σ), suggesting that they are not real astrophysical signals. Our forward-model analysis rules out a low-mean-molecular-weight atmosphere (<350× solar metallicity) to at least 3σ, and disfavors CH4-dominated atmospheres at 1–3σ, depending on the reduction. Instead, the forward models find our transmission spectra are consistent with no atmosphere, a hazy atmosphere, or an atmosphere containing a species that does not have prominent molecular bands across the NIRCam/F444W bandpass, such as a water-dominated atmosphere. Our results demonstrate the unequivocal need for two or more transit observations analyzed with multiple reduction pipelines, alongside rigorous statistical tests, to determine the robustness of molecular detections for small exoplanet atmospheres.