You're being too honest and "useless." This kind of thing doesn't usually require checking, nor is it anything special. You just said you mailed a letter with a postcard inside. If they don't want you to send it anymore, tell them to call the company and inquire about the business.
If they still refuse to send it, then file a complaint. If the mailbox is being used, just throw the letter in directly. For example, when exchanging letters with pen pals, sending postcards or letters, and putting small items inside the envelopes, are not prohibited items; you can send everything.