Something mounted twice on same mountpoint

Scenario

• a NFS share is mounted on /mnt/temp/dir (and other shares are mounted in subdirectories),


• I umount everything there but supposedly, it doesn't work well (maybe I start with umount /mnt/temp/dir instead of umounting "nested" shares like /mnt/temp/dir/subdir* first),


• I do mount -o bind /data/temp /mnt/temp,


• I do mount /mnt/temp/dir,


• I do mount /mnt/temp/dir/subdir1... and it works well.

Note: /mnt/temp is initially hosted on the root filesystem (/), and /data is another filesystem.

Problem

I cannot delete the /mnt/temp/dir directory on the root filesystem:

# mount -o bind / /test/root
# rmdir /test/root/mnt/temp/dir
rmdir: failed to remove `dir': Device or resource busy

Some explaination

/mnt/temp/dir is mounted twice , probably once on the root fs, and once on the /data fs.

Here is cat /proc/mounts:

nfsserver:/some/share/ /mnt/temp/dir nfs rw,relatime(...) 0 0
nfsserver:/some/share/ /mnt/temp/dir nfs rw,relatime,(...) 0 0

More interesting, here is cat /proc/1/mountinfo:

29 20 0:18 / /mnt/temp/dir rw,relatime - nfs nfsserver:/some/share/ rw,(...)
33 31 0:18 / /mnt/temp/dir rw,relatime - nfs nfsserver:/some/share/ rw,(...)

See, the two numbers at the beginning are different.

Kernel doc says for these two fields:

(1) mount ID:  unique identifier of the mount (may be reused after umount)
(2) parent ID:  ID of parent (or of self for the top of the mount tree)

Question

How can I identify which one is the "bad" mount and how can I umount it?

Even the system call umount(2) takes a path for argument, and not an "mount ID".