  Recent cosmological analyses with large-scale structure and weak lensing
measurements, usually referred to as 3$\times$2pt, had to discard a lot of
signal-to-noise from small scales due to our inability to accurately model
non-linearities and baryonic effects. Galaxy-galaxy lensing, or the
position-shear correlation between lens and source galaxies, is one of the
three two-point correlation functions that are included in such analyses,
usually estimated with the mean tangential shear. However, tangential shear
measurements at a given angular scale $\theta$ or physical scale $R$ carry
information from all scales below that, forcing the scale cuts applied in real
data to be significantly larger than the scale at which theoretical
uncertainties become problematic. Recently there have been a few independent
efforts that aim to mitigate the non-locality of the galaxy-galaxy lensing
signal. Here we perform a comparison of the different methods, including the
Y-transformation, the Point-Mass marginalization methodology and the Annular
Differential Surface Density statistic. We do the comparison at the
cosmological constraints level in a combined galaxy clustering and
galaxy-galaxy lensing analysis. We find that all the estimators yield
equivalent cosmological results assuming a simulated Rubin Observatory Legacy
Survey of Space and Time (LSST) Year 1 like setup and also when applied to DES
Y3 data. With the LSST Y1 setup, we find that the mitigation schemes yield
$\sim$1.3 times more constraining $S_8$ results than applying larger scale cuts
without using any mitigation scheme.
