I would say that the connotations of the word legitimate has in the line would be:
Valid and Legal
Once I was trying to learn french and I used a app called Duoligo, it helps you learn different languages for free and if you already know a bit of french, you can test yourself out and they can decide if you are a beginner, intermediate, or an expert in the language.
I hope this helped :)
A punishment is a consequence for an act of a wrong behavior.