Re: New to me and found on a New Yorker
"In architecture, a transom is a transverse horizontal structural beam or bar, or a crosspiece separating a door from a window above it."
"Transom or transom window is also the customary U.S. word used for a transom light, the window over this crosspiece."
Note the idiom is referring to the bar, not the window, thus "over the transom"
i.e it came through the window over the transom. (not "through the transom")