Top left panel: TLS spectrum of the publicly available PDCSAP detrended light curves from Sector 51. These data exhibit significant TLS power with a periodicity of 3.12 days, suggesting a potential transit detection with a prominent proximity to the orbital period of the RV-confirmed planet GJ 581 e, with a period of 3.15 days. Top right panel: TLS spectrum residuals with no signal left after a Keplerian model is fit. Bottom left panel: Keplerian transit model to the TES S data of GJ 581. Bottom right panel: phase-folded representation of the model to the data. While these data can be effectively fit with a Keplerian model, further more detailed reanalysis of the TESS data from sector 51 pointed out that the 3.12days is a marginal false-positive detection and is not related to GJ 581 e (see text for details).