It is currently not possible to remove an specific alias using QuickStatements, while it is possible to do this using the API.
For a more detailed description see https://bitbucket.org/magnusmanske/wikidata-todo/issues/114/
(I duplicated this issue here, so I can upload the patch directly to through Gerrit, so it can be easily merged)
Update: solved with https://github.com/magnusmanske/quickstatements/pull/19