Selection of given rows does not affect the saving. The easiest way to do that, is to create a subset of the data, based upon the selection, and then save that subset. (The below is corrected code: see @gzmorgan0 )
names default to here(1);
dt=Open("Report.csv");// Opening the main datafile
dt << select where( today() - In Days( 7 ) < :OUT_DATE );// Selecting past 7 days data and assigning it to P7D
P7D = dt << subset(invisible, selected columns(0), selected rows(1));
P7D << Save("P7D.csv");// Save P7D as csv
close( P7D, nosave);
Jim