This was probably orchestrated as publicity for both. Die Antwoord is on Interscope/Cherrytree, which Gaga released her first two albums through. I believe Gaga's still on Interscope as well.
They left Interscope, actually. They're on their own label now.
This is all sort of immature. I mean, Lady Gaga told them she was a fan and asked them to open for her. They could've just said no and end it there. I don't see the need to start some beef.