Turns out, I went to her desktop PC and checked Outlook. All of the contacts were still in there from her Outlook.com account, despite being deleted on the web.
So I got rid of them and the Surface...

Done that. Even if I uncheck the Outlook account each contact still shows the fact (untrue) that there is an entry in iCloud and also a linked entry on Outlook.

Hi everyone, I upgraded my wife's Surface 3 to W10 on Friday and the good thing is that now I can add her iCloud account to the People App.
I logged into her Outlook.com account on the web and...