CAUTION: is of course warranted. We are assuming this server is protected behind your firewall and walled off to only allow those API requests from potected server to server.
The Jetty server for Carte is configured for basic auth by default. The user and password configured in the carte-config.xml or as a separate list of users. If this is server to server, the API call would be seen as a service account and you simply configure that service in the carte-config.xml. You could try blank values to see if that gets you through.
However, if you truely want to go down this route, you could disable authentication at the Jetty server. That is outside of our software and you can search for that separately. As Juan Sierra Pons mentioned, posting your carte and jetty config files would be key here.