How do you think the landlord accessed the mailbox when you did not return the keys to the mailbox?
It is true that the US Postal Service does not service mailboxes that are the private properties of their respective owners.
However, without keys to access the mailbox, the landlord likely did have to call a locksmith to gain access to the mailbox.
You can call a few locksmiths to get quotes on how much they would charge to open a mailbox and re-key it.
Lock kits for common types of mailboxes are available in hardware stores for about $10 to $15 dollars. Changing the locks is not all that complicated if there is access to the mailbox. (I gained access to my office's mailbox by asking the mail carrier to open the mailbox.)
If your mailbox is more specialized, the lock may have to be special ordered and may cost more.