The long-wavelength correction (LWC) of SWOT data is intended to reduce errors related to the stability of the SWOT antenna and its attitude in orbit, especially those errors related to the roll of the satellite.The algorithms used to compute the LWC utilize SWOT KaRIn sea surface-height (SSH) measurements and additional data, and the LWC may abosrb geophysical SSH into the correction. Different LWC algorithms are used on the L2 and L3 SWOT products, which are analyzed here during the 1-day repeat (Cal/Val) mission phase lasting approximately 100 days. During this mission phase the SSH anomaly (SSHA) computed using the L3 LWC is much more realistic than the L2 LWC, shown here by comparing spatial statistics of the L2 and L3 products.The L3 LWC algorithm is nonlinear insofar as it depends on second-order statistics of the SSHA and multi-satellite SSHA differences, making it difficult to quantify the extent to which it could absorb baroclinic tidal signals. To overcome this difficulty, a proxy L3 LWC algorithm is developed which mimics the L3 LWC but is strictly linear in the SSHA. The proxy LWC is applied to the predicted internal tide available on the products, and it is found to absorb roughly 5% to 10% of the variance of the internal tide; although, this figure varies strongly depending on the magnitude and orientation of the tidal waves.