How do I delete a single file from a tar.gz archive

You can repackage it like this:

tar -czvf ./new.tar.gz --exclude='._*' @old.tar.gz

I used ._* to remove all ._files, but you can use any pattern you like, including a full path, directory, filename, or whatever.

As mentioned in the comments it's not possible to remove the file using tar, but you can exclude the file when extracting:

tar -zxvf file.tar.gz --exclude "file_to_exclude"