But then there would be a bit of a Streisand effect - as it draws attention to their lack of a non-phone tool to control their expensive headphones.
If they were to just shut Boze down, then they'll have angry customers.
If they were to create their own version of the tool, then most people would be happy.
If they were also prepared to give the Boze creator a fraction of the money earmarked for their lawyers, to pull the app and point to the official one - then everybody's happy.
To the corporation, the value of protecting their trademark vastly outweighs any profit loss from pissing off the couple of hundred people who are using this app (who, coincidentally, already own Bose headphones).
If they were to just shut Boze down, then they'll have angry customers.
If they were to create their own version of the tool, then most people would be happy.
If they were also prepared to give the Boze creator a fraction of the money earmarked for their lawyers, to pull the app and point to the official one - then everybody's happy.