Permissions issue XFCE remove desktop items
 

I'm on Debian.
It is impossible to delete items on my desktop via Thunar, a terminal or right-clicking. I want to understand the problem before brute-forcing it.
The permissions for all files on the desktop look like this: -rw-r--r-- 1 usrname usrname.
No group write permissions. Is that a problem? Why so? And then why is it configured like that? (Was it probably something I did myself? :-X )
The permissions for the folder itself look like this: dr-xr-xr-x 4 usrname usrname.
Beginner explanation appreciated.

I suspect the problem is the lack of write permission on the Desktop dir. Here is what mine looks like, I can delete icons in the folder at will.

Add write permission to the Desktop dir and see what happens.

It was indeed the permissions of the directory. Also it is very likely something I had done myself. (In fact I have restored it so nobody saves anything on the desktop.) I still don't understand the difference between user and group, but I guess that is out of the scope of this question.
For those who are clueless:
chmod u+w Desktop
rm Desktop/That_file.desktop
chmod u-w Desktop