The Widowed Parents Allowance is treated as income in calculating entitlement to Tax Credits, but I believe it is considered to be Pension Income and because of this the first �300 per year is ignored. However, your friend clearly will have been overpaid. The sooner she lets HMRC know the position the better. She will need to tell them the total WPA she has received for each tax year.
She will have to pay back the overpayment but it is possible that this will be done by reducing the amount of her ongoing tax credit payments rather than her having to pay a lump sum.
A lot of people do get overpaid tax credits for a variety of reasons and there is no reason why she should get into trouble about this. She will just have to explain that when she completed the forms she did not understand that the WPA had to be included but she has now been told this is the case.