You're envisaging that an impact on the Moon causes enough mass of ejecta that the amount impinging on the Earth's atmosphere is enough to do
... something significant? Or that a single impactor of sufficient size is ejected from the lunar impact which could then impact on a city/ county/ state/ country/ continent and obliterate it?
The latter case is pretty implausible : you'd want an ejectum of several kilometres diameter to be a worthwhile opponent. The 50-odd metres of the Barringer impactor really isn't enough to wipe out much more than a small city. Particularly the sprawling cities of America. To get an ejectum from an impactor, you need a very large shear rate, which only occurs in a small range of angles from the axis of the impactor. (Unless you've got a very grazing impact.) So you're unlikely to have a big enough volume to generate such a large impactor. And you'd get a much larger volume of smaller ejecta generated at the same time.
Producing lots of "Chelyabinsk" or "Tunguska" like air-bursters ... that's a more credible situation. But it'd still need a fairly large impactor, and they are the less common ones. And I think that they're more likely to impact the Earth than the Moon (and then spray the Earth with secondary ejecta).
But to be honest, I'd lose more sleep over the big impactor headed directly for Earth than the effects of secondary ejecta from a Lunar impact. And I do pay attention to these things, looking at the (literally) astronomical chances of them happening and affecting me, and I don't lose sleep over that (being far enough inland and up-hill to not worry about a distant ocean strike).