  We describe the data processing of the Survey on extragALactic magnetiSm with
SOFIA (SALSA Legacy Program). This first data release presents 33% (51.34h out
of 155.7h, including overheads) of the total awarded time taken from January
2020 to December 2021. Our observations were performed using the newly
implemented on-the-fly mapping (OTFMAP) technique in the polarimetric mode. We
present the pipeline steps to obtain homogeneously reduced high-level data
products of polarimetric maps of galaxies for use in scientific analysis. Our
approach has a general design and can be applied to sources smaller than the
field-of-view of the HAWC+ array in any given band. We estimate that the OTFMAP
polarimetric mode offers a reduction of observing overheads by a factor 2.34,
and an improvement in sensitivity by a factor 1.80 when compared to previously
obtained polarimetric observations using the chopping and nodding mode. The
OTFMAP is a significant optimization of the polarimetric mode of HAWC+ as it
ultimately reduces the cost of operations of SOFIA/HAWC+ by increasing the
science collected per hour of observation up to an overall factor of 2.49. The
OTFMAP polarimetric mode is the standard observing strategy of SALSA. The
results and quantitative analysis of this first data release are presented in
Papers IV and V of the series.
