I didn't even notice the missing 'to'! My explanation is for the term "to have little to do with something", which I took to be the question.
I guess from Mike's response, they don't use the term in AmE - unless being American has little to do with his response. Maybe he means that he still can't understand the example sentence - nor can I - rather than he can't understand the [incomplete] idiom in the title, or the question.