Tente isto:
for f in *.bil; do
n=$(echo "${f}"|sed -r 's/^.+([0-9]{8})__[0-9]{8}[.]bil$//'|grep -Ev '.bil$')
#or:
#n='echo "${f}"|sed -r 's/^.+([0-9]{8})__[0-9]{8}[.]bil$//'|grep -Ev '.bil$''
if [ -n "${n}" ]; then
mv "${f}" "${n}.bil"
fi
done