Hi Jim,
Thanks for reaching out! Ownership of the server your staging site resides on depend on how it was actually created. If you created your staging environment using BoldGrid Cloud WordPress then it would reside on our server.
If the staging environment was created anywhere else, like your web host cPanel area for instance then you would own the server environment or a third party.
Our staging sites normally have URLs that start with something like https://demo2.cloudwp.dev/trial-
. If you could link us to the URL of your staging area we can let you know if it’s ours or not.
I hope this helps Jim!