There's obviously a tech error with this. First time I got it i answered just 'blarney' and was rejected stating the correct answer should be 'The Blarney'. So this time I answered 'the blarney' and got rejected with the correct answer being 'Blarney'. I've never known Duo be case sensitive but i tend to only use lowercase for speed, but that's been the only difference. My money is on a simple tech problem anyway.
Actually this is a problem now. This is the last repeating question in a lesson. It alternates the 'correct' answer so giving the same version twice in succession should get me out of the loop without having to quit the lesson and lose all progress in it. I'm giving it a go anyway.
(Update - Yep, that worked.)
Why is Blarna lenited? It ends with a vowel, so it should be masculine.
Not all nouns ending in a vowel are masculine, e.g. comhairle is feminine. Blarna is lenited because it is feminine so you have an Bhlarna.
According to O'Reilly's dictionary blár is a plain, a field. It is a masculine noun so in the genitive case it would be bláir, e.g. cloch an bhláir. The diminutive form of blár is bláran which means a little field.
Blarna on the other hand is a feminine noun, so in the genitive case it would be Blarnan as in cloch na Blarnan.
Some folklore associated with it is given here.
Blarnán is the genitive of Blarna.
The genitive can be understood in a couple of different ways. It can be used to indicate ownership ("Blarney's Castle") or an "of" relationship ("the Castle of Blarney", which can also be an indicator of ownership) or when a noun is being used as an attribute of another noun, like an adjective ("Blarney Castle").