If you have a GameServer server you have FTP access. Download FileZilla:
https://filezilla-project.org/
Your FTP IP is the IP of your server. The port for FTP is defaulted to 21. Your username and password is usually the same as your GameServer account username/password. If not then check your account settings.
From there you can manipulate/add/remove the files on your server. You can follow this guide to set up Replays:
http://wiki.teamfortress.com/wiki/Replay_server_configuration
Honestly though, I wouldn't even bother. Replays break a lot, they're pretty unreliable, crash a lot, sometimes fail to download. Demos are better in a lot of ways. Only reason they ever existed in TF2 - along with pretty much everything added to TF2 in the last three years - was a test for DOTA 2.