MichikoQ,
The Connections Object is the correct object in the WSAPI, however, it is not editable in Agile Central, which is why there is only the GET request. Below is a line from announcement of this feature, Product Announcement - Third Party Context in Agile Central,
Please note that Third Party Context data is non-editable, since the external source is the source of truth. You can access the Third Party Context Help Page here.
As this is currently in Beta, you may provide your feedback to the Product Owners via the Feedback button on the Third Party Context page.
Please let us know if you have any further questions.
Michael