Most of these cartoons must be NYC-centric, because I don’t get half of them.
This one, OTOH, makes me crack the hell up. 
To be clear, I don’t picture the woman as actually making a date, but as turning one down. Some creep has called her up to ask her out, and she’s telling him “Never”.
And kayT, if that cartoonist was actually attempting to draw what he said he was drawing, then he has no talent whatsoever. The “naked woman” looks like she’s wearing an unflattering dress, and the “female guest” looks like a man in a business suit.
Thurber wasn’t a great drawer … umm … draw-er … uhhh … He wasn’t very good at drawing, but he got the job done. And the guest is a man in a suit. When Thurber said it was two women, he was clearly misremembering. Maybe about the nudity, too.
Personally I have always found it very endearing that Thurber could not draw in a conventional way; seemed to add a certain something. And he certainly knew he couldn’t draw lifelike images and did not really try to do so.