The Complimentary ID is mailed to Link from Beedle after Link has purchased 30 items from him. After his 30th purchase, Link will be able to find the Complimentary ID in any Postbox. The Complimentary ID is a one-time use item. When given to Beedle, he will "compliment" Link for his continued patronage, which will fully recover all of his Hearts.
"You got the Complimentary ID! Who knows what this is, but apparently you should take it to Beedle... Keep it in your Delivery Bag for now."