When I perform branch -a:
$ git branch -a
* master
remotes/origin/HEAD -> origin/master
remotes/origin/hello
remotes/origin/master
To delete a remote branch, use
git push origin :remotebranch
Everything else operates on the local repository only. In more recent versions of git, you can also
git push origin --delete remotebranch
As per the documentation, --delete means the same "as prefixing all refs with a colon".
If you are wondering about meaning of the :, it follows the standard syntax for push. Usually, you would write
git push origin localbranch:remotebranch
but here, you replace localbranch with "nothing", effectively deleting the remote branch.