well, I was gonna say to use X11, another feature that you can use with putty to download files. I've read about it but never tried.

But wait, so you want to copy files to windows right? Windows is GUI, if you can use Putty, why can't you use winscp? You can use the same login credentials to run winscp. Winscp is like ftp. It's not like putty. You still need to use putty to do things. And you don't need any privilege to run winscp, it just downloads and run it. I don't know if you can download if that's what you are talking when you said privilege.

Here is a tip. What would I do if I were you.
1. I'm assuming you have a separate personal webhost somewhere. Enable ssh access to that webhost. Connect from your current linux to your webhost via scp, share files as you wish.
2. Back home, use winscp on your own computer and transfer files to/from your webhost.
3. At work, use your linux machine to download files from your personal webhost.
Bit tedious but it always works for me.