It allows you to play for Bilbao in the the first place - they have a strict 'Must be Basque' policy - though they stretch that to the limit - basically playing as a youth in a Basque region (and there are 3 departments in France adjacent to the Pyrenees that count) or a great grandparent who is Basque.
It matters as they don't have many other player options and don't let players go easily. They'd rather lose the money and keep the player. Typically the player has to force the move to leave.
Grandparents being Basque isn't enough, let alone Great-grandparents.
Tommy Oar's proposed move to Athletic Bilbao fell through after the club deemed that the winger did not possess significant Basque heritage.
The Australian thought he could be eligible to play for the club thanks to his paternal grandparents being from the region, but Athletic only allow players born in the Basque Country or those who have come through the junior ranks to represent the club.
Despite the heritage, the 25-time capped Australian international, was told he was not eligible to represent the club
http://www.itv.com/news/2015-08-18/athletic-bilbao-reject-tommy-oar-over-insufficient-heritage/
The Australian thought he could be eligible to play for the club thanks to his paternal grandparents being from the region, but Athletic only allow players born in the Basque Country or those who have come through the junior ranks to represent the club.
Despite the heritage, the 25-time capped Australian international, was told he was not eligible to represent the club
http://www.itv.com/news/2015-08-18/athletic-bilbao-reject-tommy-oar-over-insufficient-heritage/