You need to look a little bit deeper in /tmp/tmpmount/mnt:
du -h -d1 /tmp/tmpmount/mnt
You can access files under /tmp/tmpmount/mnt and either delete them or move them to their proper mounted filesystem under /mnt. Either one will free up space on your root filesystem. Simple, crude examples:
mv /tmp/tmpmount/mnt/backup02/somefile /mnt/backup02/somefile
or
cd /tmp/tmpmount/mnt/backup02
rm -r *
Just be careful. It’s really easy to get confused about what paths are in the physical root filesystem vs. paths in other mounted filesystems. You might use the df command just to confirm what the physical device is:
df /tmp/tmpmount/mnt/backup02
vs.
df /mnt/backup02
The first should show the filesystem “/dev/mapper/rl-root” that holds your root filesystem. The second should show your external backup drive “/dev/sdb1”.