Tá uirthi ... can mean "She must ..." or "She has to ...". But that's just idiom, (and the same idiom exists in English - "It's on me to ....").
But Tá ... uirthi doesn't mean "she has ...", it means "... is on her", which is the idiom used in Irish for describing features like this - and it also exists in Hiberno-English - "Did you see the big ears on that fellow?" - "He'd a face on him that'd break a mirror", etc.
At this time the translation "Her hair is dyed." is not accepted as a correct response here, even though a similar construction is accepted in other examples in this lesson. Perhaps this is just an oversight? Actually this might be a more accurate translation, since it is possible that the dyed hair she is asserted to have in the official translation could just be a sample swatch from her haircutter. :-)}