DWP mistakenly thinks I'm in hospital (PIP) will they correct underpayment?

Hi guys, I was awarded pip backdated from 28th August. In my assesment I told them I was in hospital 24th sept to 2nd Oct.

Instead of recording this they have mistakenly recorded instead of this that I have been continually in hospital since October 22nd. It says this on my award letter I received in November but I didn't realise this was the case untill today when I checked and l I haven't received any pip payments outside of the initial one.

If I call them to fix this will I get paid the underpayment they owe me (it will be arround £700) when they correct it as it was their error?

I have not had pip before sorry I don't understand it well. I am really worried about missing out the money due to their error but the award letter was confusing so I literally didn't realise they thought I was in hospital still/got the dates wrong untill now so I didn't call to correct.

Thank you

Edit: to those who didn't read this properly DWP owe me money due to their error I'm asking if I will get it back or if they will be difficult as I have heard stories!!