chmod/chown hfs+ Volume
Part1:

Maybe, you will need repair permissions - easily done with Finder.


press CMD-I on the top directory where are your files in the external HDD
click on the lock symbol (right bottom corner)
enter your password
and adjust the 1st line at the permission section (Me) for "Read &amp; Write", and from the cogwheel select "Apply to enclosed items..."


The above should repair permissions - but - probably will not help (as you already told)

Part2:

If the part1 not helped, probably (and only maybe!) you have an broken ACL list. (because files are copied at another OS). OS X HFS has not only usual chmod modes, but maintain ACL (access control list) too.

Try this in the Terminal.app - DON'T copy&amp;paste all at once, enter the commands one by one...

cd /Volumes/MOUNT_POINT/directory/with/the/backed/up/files
# where MOUNT_POINT is the drive name as appears in the Finder.  

pwd
# DOUBLE CHECK the pwd
# if you do the next on the wrong place - you can corrupt your system
# YOURE WARNED!!!

#this will remove all ACL informations recursively from all files in your current dir
sudo chmod -RN ./*

#this will change recursively the ownership of the files -&gt; to you.
sudo chown -R $(whoami) ./*    #change ownership of files to you

cd      # go home


now you can quit Terminal.app and check access to files via Finder and you should repeat the first part - changing permissions via Finder's -> CMD-I ...