Unique Identifier/Credit Newb, apologies if this is a dumb question. If a bitcoin is sent to my wallet is there a way the sender can use any part of the blockchain/transaction as a unique identifier so they can claim a credit in the future for the amount sent, that is, without assigning them any additional identifying information to them? (e.g. You send me a bitcoin, I treat it as a credit.  You can claim the credit by using some combination of the numbers used in the transaction, so I can credit you the amount sent, without assigning any additional information to you, and no one else could be privy to that identifying information.  Thank you for the help!
This is possible, but your customers will have to use a wallet that supports the functionality of signing messages using the wallet’s private keys. For example, bitcoind has the signmessage command. The user could input a message such as ”todays date is ____, and I control bitcoin address ____, which sent coins to ____ service” in order to prove their identity. 

Using any identifying info from the transaction itself will not be a good way to prove user identity, since all transaction details are a matter of public record. 

Note: By utilizing this functionality, you will be restricting your potential user-base to only more knowledgeable users. Not all wallets have this functionality, in fact most do not. If a user happens to sends bitcoin from a wallet that cannot sign messages, they can prove their identities by importing the private key into some other software that is capable and then using it to sign a message— but again this is a more ‘advanced user’ sort of operation. 

Another note: DO NOT build a service which requires users to communicate their private key to you. This would be an irresponsible thing to do.