Adding a hosted service to a web mapping app requiring a Server service

[WendyProudfoot]

I am hoping to be able to add an ArcGIS Online hosted service to a web mapping application outside my workplace, that requires the URL format of an ArcGIS for Server service.  I am not even sure if this is possible.

The web mapping application is ESRI-based, and is the product of a partner organization to my own workplace.  In the past, we have successfully added our data to the web mapping app via ArcGIS for Server services, but I am experimenting to see if we can add our data via ArcGIS Online hosted services.  The web mapping application is set up to detect when a URL is not in the format of a Sever-based service, so I get the error message in the screen capture attached.

Does anyone know if there is any possible way to accomplish this?