PIP, mental health & mobility, no backdate due to tribunal

Hi, I received a letter from the DWP over the issue of PIP & mobility due to psychological distress.

I have serious mh issues but was turned down for all PIP (I previously had DLA higher rate care, lower rate mobility).
When I went to tribunal they awarded care component but not mobility - even though I my mobility is severely restricted by psychological distress that I had provided evidence for.

When the issue of mental health & mobility was reviewed in DWP I was hopeful at getting this rectified. However my letter from them says that bc my PIP award was decided at tribunal, and because the DWP cannot overturn anything decided at a tribunal, that they are unable to award me it (unless I get reassessed and then I still won't get the backdated payment).

My question is ... the tribunal's decision presumably has to be based on the benefits criteria and guidelines issued by the DWP. So if the guidance on the issue was wrong (ie incorrectly ignoring the impact of distress on mobility) then how could the tribunal award otherwise?

I have had the DWP letter for some time now, as I am unsure whether the raise this or not. But the more I think about it, the more I am questioning the validity of their decision.

Thank you for reading