There is supposed to be a public relations front that comes under the Section VII umbrella. That may be why it says finance, but it isn't accounting based on anything else they have as department/section responsibilities.
Here's what the Fans from UNCLE page says:
Section VII: Public Relations and Propaganda
U.N.C.L.E. does have a public relations front.

There may have been a bit of floundering when producing things like the ID card.