To delete a bookmark from a remote server, you must have permission to push to the server. If you can push to it, then you can:
hg bookmark --delete <bookmark name>
hg push --bookmark <bookmark name>
See the “Working With Remote Repositories” section of the Mercurial BookmarksExtension wiki for further info.
NOTE: This only removes the bookmark itself. It does not remove any changesets that were associated with the bookmark. If you need to remove the changesets themselves, then you must consider other methods as noted in these related questions.