Rename a git tag old to new:
git tag new old
git tag -d old
git push origin :refs/tags/old
git push --tags
The colon in the push command removes the tag from the remote repository. If you don't do this, git will create the old tag on your machine when you pull.
Apparently this also removes the linked release.
EDIT:
It might not entirely get removed. If the release is gone, open https://github.com/ACCOUNT/REOO/releases/tag/OLD. If the link work you might be able to see the linked release there. Open it and edit the release to use the new tag instead.