Currently, ypu,do not have a case against them to seek what you call the outstanding amount.
That amount has never been agreed or accepted as due to you.
Your options are to either accept what they are offering or decline the payment and take out your legal action against them for the amount you feel you,wish to claim for.
Remember, if you loose the case, or even if you win, a court may not award any extra. Yo could also face legal costs for both sides.
I would advice that you visit a local civil litigation law firm as a private client and seek person legal advice on this matter. I can only provide general,advice here not person private advice.
If you take the case further and loose or a court rules in your favour, the court could as I say still award costs to,the other side especially if the court does not increase the amount etc. You could end up,paying not only your own costs but also those for,the other side.