Old question but a newbie, like me, might struggle with it.

So I created a directory, Production, then later renamed it production. My original files were stored in Github under Production, all new ones in another directory production. When I worked locally, (windows), it was all fine under production.

Sounds just like what you are asking.
Simply fix really, ignore all the git stuff.
Rename your local directory something else, let's call it test. Commit and push. All of your files and directories will be aggregated under the new directory test. Rename it back to your lower case, production, and commit and push. All issues resolved.