The data service for TeamPulse is a WCF Data Services implementation. We currently do not provide any documentation (we will be releasing an API in the future), but because this is a RESTful service you can inspect it and query it to your leisure.
To help with your specific request, you could determine the completion time of a story with a query against the Audit table within TeamPulse. This table tracks all changes to all entities within the application on a row-per-property level. So in your case (assuming you are using the default TeamPulse project template where a completed story would be marked as 'Done'), you would be looking for rows where the TableName is equal to 'Story', the FieldName is equal to 'Status', and the NewValue is equal to 'Done'. You'd also likely want to filter by ProjectID, which you can find within your normal TeamPulse URL when accessing the project.
To make the above call in your browser using a RESTful query, you could use a URL like this (where localhost is the name of the machine TeamPulse is installed to):
Hopefully this can get you started in extracting the information you require. If you have any further questions please let us know.
All the best,
the Telerik team
Do you want to have your say when we set our development plans? Do you want to know when a feature you care about is added or when a bug fixed? Explore the Telerik Public Issue Tracking
system and vote to affect the priority of the items