They will need to have a copy of the TRILOGI software in order to run the TLServer. Once the TLServer is running on their computer and if the PC has direct link to the internet then you can use TRiLOGI to remotely program the PLC via the TLServer.
However, if the PC running TLServer is behind a corporate firewall /NAT router then the network administrator would have to configure that PC to allow it to be accessible via the Internet before you can do that. There are some description of this issue in the TLServer help pages.