QTS Elligibilty error now invoiced for bursary repayments

Freeasthewindblows

I am writing on behalf of my friend, who is Spanish. I am going to call her Sue. 
Sue has a masters qualification in Secondary teaching from Spain and came to England to pursue a career as a Spanish Teacher. In order to teach here in UK, Sue needed a QTS qualification and so applied for one in 2016. The department for education responded that Sue was not eligible so Sue was left with no choice but to study the PGCE in order to obtain the QTS so Sue could teach. 
To be accepted onto the PGCE course, the entry requirement was to have two referees from two different placement schools and 7 points in the IELTS English exam. 
Sue went on to study for the exam and to find schools she could get references from. This took a lot of time, stress and money and eventually was accepted onto the PGCE course in 2020/2021 and left her job to do it. 
Sue received £7800 between September and December from the Department of Education. 
With various circumstances occurring including the Coronavirus pandemic, Sue was left with no choice but to withdraw from the PGCE on the 9th of December. 
Not knowing what to do, on the 17th of December Sue took a chance and applied for the QTS again and this time was successful.  
Sue is now receiving invoices from the University for the full amount of £7800. The University claim they are chasing the money up on behalf of the department of Education. Because Sue is eligible for the QTS, she has no right for the bursary and must pay back the full amount. 

After numerous attempts to contact the Department of Education there has been no contact from them regarding their mistake about the QTS certificate only invoices via the University. 

The question is should Sue have to pay back the £7800 when The department of Education made the mistake about the QTS eligibility.  Sue wouldn't have spent 4 years trying to obtain the QTS via the PGCE and will this effect her credit score in the future? Any advice on how to approach the department of education to recognise their error and come up with some contingency plan.  

Voyager2002

The best way to get an intelligent answer from the DfE (or any government department) is to contact your local MP. (When an MP's office contacts a government department, the issue is given priority and is dealt with by someone relatively senior.)

If you don't like the answer that comes back with the help of an MP, you can ask your MP to refer the matter to an offical called the Parliamentary Ombudsman, who has authority to review all decisions made by government departments, but only when an MP refers the matter.