I am struggling to pass ConnectionString when deploying AzureRM Web App in TFS Release Manager. I have tried to put the ConnectionString in the "Additional Arguments" field and provided the correct variables from the "Variables" section. However, I am getting the following error:
[error] Error: Unrecognized argument '-connectionString'. Error count: 1.
Does someone have experience in how to set up ConnectionString when working with AzureRM Endpoint to deploy Web Apps? As far as I know, the approach described above works fine when using Azure Web App Deployment with Azure Classic Endpoint.

You could also try to use some 3-party extension such as Azure WebApp Configuration task.
This task reads VSTS/TFS variables and adds those as AppSettings and ConnectionStrings to an Azure WebApp.