  We use the Beyond Ultra-deep Frontier Fields and Legacy Observations
(BUFFALO) strong lensing image catalog of the merging galaxy cluster Abell 370
to obtain a mass model using free-form lens inversion algorithm Grale. The
improvement of the strong lensing data quality results in a lens plane rms of
only 0.45 arcsec, about a factor of two lower than that of our existing HFF v4
reconstruction. Since the number of images is nearly the same in both, we
attribute the improvement to the improvement in the data quality. In our
reconstructed mass model, we found indications of three distinct mass features
in Abell 370: (i) a $\sim\!35$ kpc offset between the northern BCG and the
nearest mass peak, (ii) a $\sim\!100$ kpc mass concentration of roughly
critical density $\sim\!250$ kpc east of the main cluster, and (iii) a probable
filament-like structure passing N-S through the cluster. While (i) is present
in some form in most publicly available reconstructions spanning the range of
modeling techniques: parametric, hybrid, and free-form, (ii) and (iii) are
recovered by only about half of the reconstructions. We tested our hypothesis
on the presence of the filament-like structure by creating a synthetic cluster
- Irtysh IIIc - mocking the situation of a cluster with external mass. We also
computed the source plane magnification distributions. Using them we estimated
the probabilities of magnifications in the source plane, and scrutinized their
redshift dependence. Finally, we explored the lensing effects of Abell 370 on
the luminosity functions of sources at $z_s=9.0$, finding it consistent with
published results.
