It is always a problem to grab a remote database onto a different remote computer. For this purposes, our institute uses Handy Backup (for Firebird-based apps, too), but if you are preferring GBAK, these are some more ways to do it.
A simplest method is to call directly to a remote database from a local machine using GBAK (I see it was already described before me). Another method is an installation of GBAK to a remote machine using administrative instruments for Windows networks. This method can be tricky, as in mixed-architecture networks (with domain and non-domain sections) some obstacles are always existed.
Therefore, the simplest method is writing a backup script (batch) file calling GBAK and then copying the resulted Firebird file to some different network destination, using a command-line network file manager or FTP manager like FileZilla. It require some (minimal) skill and research, but can work for many times after a successful testing.
Best regards!