blow-in card

noun

: a card printed typically with a subscription offer or advertisement that is inserted loosely by a machine using air pressure between the pages of a magazine

What demon dreamed up "blow-in cards"—those subscription cards that drop out of a magazine as you pick it up to read? Reportedly a machine, at some stage in the mailing process, riffles each magazine's pages and blows in anywhere from one to six of these cards. The method a cheaper than stapling the card in, and presumably the dropping-out process forces the card on your attention.—

Alan L. Otten, Wall Street Journal, 21 Nov. 1974

Inside the magazine there were lots of blow-in cards offering subscription deals, but he didn't want to have to fill out a coupon and mail it in and wait six weeks for his subscription to kick in.—

Harvey Mackay, Albany (New York) Times Union, 13 Apr. 1997