Currently we provide a way to export selected items' information from almost all TeamPulse screens. You need to select the columns you wish to expose and then export in the desired format.
You can also export each of the reports and in your case Details report could be useful - check attached screenshot.
In regards to timeline exporting, at the moment we do not provide such functionality, but I will add feature request in our TeamPulse project. Do you imagine having export button on View Schedule screen, which would export the timeline graph, or a separate report including graph and the items assigned to the selected period?
the Telerik team