Unable to delete files

I am unable to delete some files and directories which exist under /mnt, presumably because symbolic links were created during mounts (just guessing...)
When I attempt to delete (as root) various files and directories, I get an 'Operation not permitted' msg. Even booting from a different device and mount that directory does not permit removal of these files.

Any suggestions as to how to delete them?
Impossible to say without knowing how the remote file system got mounted. This is most likely a problem on the remote host.

(edit): By default /mnt is empty and it's only used to mount other file systems on it.

(edit2): Look into /etc/fstab and/or the output from mount, that should give you some more hints.
A: Are you root? Obviously I know that you are balanga and not root, so my real question should be: is your id zero?

B: What is the ownership of the files, what are the permissions of the files, and what is the id and group membership of your process?

C: What type of files are they? Are they regular files, pipes, soft links, purple flying elephants, mount points, ... ? If the file is an elephant, make sure it doesn't fall on you when you delete it.

D: If they are mount points, or on a separate file system: What type of file system, and is it a remote file system? Does the remote file system use some sort of id or permission translation system?

E: Do the files have ACLs? In that case, what do the ACLs mean (that depends on the type of file system)?

By the way, I buried a few jokes in the answers; some days I think that the only way to not go insane when administering computers is humor.