by Ken Task.
The only clue we have that the system ls linux is in the error reported ... '/''s leaning to the right. We do not know what distro so the suggestion below would have to be adjusted for your Linux distro.
Think the error is telling you exactly the issue: not enough liberal permissions on moodledata directory and all the subdirectories files contained therein. Since moodledata isn't/should't be directly accessible to anyone using a browser (not logged onto Moodle), that directory could have more liberal 'write' attributes.
From command line think I'd:
chmod ugo+rw /var/moodledata -R
That allows user, group, an 'others' read/write (which should also include the ability to create directories on moodledata and all of it's contents (the -R - recursive).
Then try your backup again.
'spirit of sharing', Ken