Hi,

I too have faced these type of hack issues from my webhosting servers. Which is quite natural that we cannot avoid. So, now you are in a loop.
1) Do you have an local backup or else do you have a separate server for the backups?
2) What is the format of the backup files?
3) You can use the Netcat command to transfer the files from one server to another. Here below the link

A Unix Utility You Should Know About: Netcat - good coders code, great reuse

Or else you can use the rsync command to transfer the files from one server to another in a quite time rather than upload and download.
4) I hope that every thing is been clear on the documentation, on how to restore from the backup.