Maybe the GOP should try to shame the Dems into some sort of symbolic sanctions against Obama if he doesn't knock it off....? Just a thought. It might draw enough negative attention to the Democrats to further mess up their 2018 aspirations.
Trump's team will do something about this. They have to. Trump cannot have Obama stalking him, like a jilted girlfriend, and meeting with all the people he is meeting with.
Trump's administration may quietly call foreign leaders that Trump is expected to meet with, and ask them not to meet with Obama. "Listen, as soon as this goes public Obama is going to try to meet with you. We strongly request that you do not indulge him."
You would think that this would never be necessary, but with Obama anything is possible. One thing we know is that Obama will never follow Trump to the Middle Eastern countries. The Muslims 'hate' Obama mostly because of his support for the Muslim Brotherhood terrorist group which is outlawed in most M.E. countries. They would likely not let him in.