I have this script which will list files back 8 days, but I don't know were to add the remove command. See script below.

OFFSET=${1:-8}

case $OFFSET in
*[!0-9]* | ???* | 3? | 29) print -u2 "Invalid input" ; exit 1;;
esac

eval `date "+day=%d; month=%m; year=%Y`
typeset -Z2 day month
typeset -Z4 year

# Subtract offset from day, if it goes below one use 'cal'
# to determine the number of days in the previous month.
day=$((day - OFFSET))
if (( day <= 0 )) ;then
month=$((month - 1))
if (( month == 0 )) ;then
year=$((year - 1))
month=12
fi
set -A days `cal $month $year`
xday=${days[$(( ${#days[*]}-1 ))]}
day=$((xday + day))
fi

print $year-$month-$day
print $month/$day/${year#??}

ls -l /feeds/repository.dir/*$year$month$day*
ls -l /first_value.dir/Download/validated.dir/xxx.xxxx.*$year$month$day*
ls -l /feeds/vlink_backup.dir/hsl.dir/xxx.xxxx.*$year$month$day*
ls -l /feeds/vlink_backup.dir/processing.dir/*$year$month$day*
ls -l /feeds/vlink_backup.dir/sch.dir/xxx.xxxx.*$year$month$day*
ls -l /feeds/vlink_backup.dir/sum.dir/xxx.xxxx.*$year$month$day*
ls -l /feeds/vlink_backup.dir/unl.dir/xxx.xxxx.*$year$month$day*