She apparently came on a visa called Fresh Talent, which was exclusive to Scotland, to allow people to work 2 years post-study.
Her two years were up. She was in need of another visa, such as Tier 1 (formerly known as HSMP, Highly Skilled Migrant Programme), Tier 2 (employer-sponsored) or Tier 4 (student). She needs another visa to remain here. There is no more Fresh Talent and she needed to sort out which visa to apply for before it expired, hence, whatever visa she applied for has been denied and she is currently in the appeals proces.
Additionally, on the visa she was on, it is clearly 'NO RECOURSE TO PUBLIC FUNDS'.
If you Google, 'What are public funds', the first hit is a definition, the second is a bullet-pointed list straight from the UKBA stating that Working and Child Tax Credits are public funds.
Additionally, when you complete a Tax Credit application form, in one of the very first posts is an area where you need to declare if you are subject to immigration control and further explanation in the notes.
This is not hard information to find, that WTC is a public fund and if your visa excludes the use of public funds.
The onus is on the visa holder to make sure they are not violating the terms of their visa.
Furthermore, Gamu needs her own visa, as she is now too old to be a dependent on her mother's visa.
So, TV show contestant or not, not really bothered with people who don't have a proper visa being removed. If they have political concerns they should declare themselves asylum seekers. But the initial visa on which Gamu's mother extended her stay was for economic migrants and was never meant as a path to permanent residency.
There's nothing to say they cannot re-apply from their country of origin and re-enter.