Screen shots don't appear in forum posts, so if you need us to see it, you'll have to post it elsewhere and put a link here. (External links may get you post held for moderation, though!)
If the remote repository is not itself broken, just out of date, I would suggest you pull a new copy into a new local folder, then move your current source files into the new copy and commit. (But if you changed any build settings, you'd have to re-do those manually.)
Or, if you have a local folder from which .git has been deleted (as you said you did), you can create a new repository from the git command line by cd'ing to the project directory and issuing a "git init". You would then need to manually add the project, then in Xcode re-add the source files.
The problem with doing it this way is that not everything in the project package should be in the repository, so getting the right set of files re-added is kinda fiddly. Starting from a fresh pull is usually easier.