It does sound like you have actually tried to do the best thing for the cat in this situation Nix, and I can appreciate it.   We "adopted" 2 stray moggies years ago, it took many months of attention to get them remotely tame, 1 eventually became a loyal loving pet, the other would never get tame enough.  They clearly didnt belong to anyone else.
If that lady did own the cat, there's no way in the world she wouldnt have SOME kind of photographic evidence of it, which would be pretty much indesputible.
However, you've taken the cat in in a pretty poor state - and if she does get annoying about it, I'd just call in the RSPCA, or advise her that you're willing to and would pursue a neglect case against her if thats the way she wants to take matters.
Hopefully she'll see sense.