Correct me if I'm wrong, but a binary search tree is a very simple data structure. It has rules, and just by it's definition, and the definition of "inverted", you should be able to come up with an iterative solution, even if it's just walking the tree and re-creating it.
It may not be the best, but it's a solution, it's a starting point.
But if you're interviewing for a job solving problems, shouldn't you be able to solve problems? Even if they aren't the best solution? Genuinely asking here, as this approach seems to have a 85-90% success rate for me.