Ok I see,
It seems there is no easy way to delete the drill hole only for a through-hole pad in Eagle. It is a though-hole pad after all. Also, Eagle is also somewhat notorious for poor milling support.
Firstly, if the drill hole is smaller than the milling slot then the engineers usually follow the milling slots or ask for confirmation. So the files should be fine - in theory. But it seems the engineer for your previous order missed the milling slots. You should be able to get some compensation for this by contacting our support and providing some photographic evidence.
I suggested removing the drill holes to guarantee this doesn’t happen again, but it seems it is not so easy in Eagle. One workaround I found is to replace through-hole objects with SMD pads on both top and bottom sides of the boards, thus eliminating the drill hole.
Hope that helps,