You should read this article: Remote branches with TortoiseGit
According to this blog post:
...remove the local branch by first opening up the
Checkout/Switch dialog to get at the
Browse refs dialog.
Browse refs dialog we can right click on the local branch and choose to delete it.
To delete a remote branch we can do the same thing, but instead of right clicking on our local branch we expand the remotes tree in the left part of the dialog and then locate the remote branch.