How can I delete saved configuration passwords from AirPort Utility for iOS?
Since iOS doesn't have a keychain utility to go in and surgically remove the stored password, you would have to either:


change the password on the base station to effectively lock out all clients with the old password.
erase the iOS device and refrain from restoring a backup that contained saved passwords onto the device. (Encrypted backups of the device typically store keychain items, non-encrypted backups don't save those passwords, so you might try an unencrypted backup, restore the backup and then test if the password was saved in the application bundle as opposed to a keychain).
As a long shot, try enabling iCloud keychain syncing and see if you can clean things on a Mac that has iCloud keychain syncing enabled as well by opening the iCloud keychain in Keychain Utility.