After an EFT using a debit card to a third party, the consumer decides the following day to cancel transaction for real valid reasons. Third party holds the funds and decides not to return funds back, is there a way the consumer can file a dispute with the financial instution for the return of said funds? Where in Fed Reg E protects the consumer? Reason I ask is that the financial institution says they cannot help. It is between third party and consumer.

I'm not an expert by any means but Reg E covers transactions that aren't authorized. In the above transaction, the transaction was authorized. The consumer has changed their mind (for whatever reason) but the bank can't persue a chargeback for unauthorized when it really was.

Unless this was a transaction that was reocurring (like AOL for example) and the consumer had called the company and revoked their authorization from future debits and a debit occurred then it would trigger an unauthorized transaction.

Curious if other banks think the same way?

You are correct. Reg E is for consumer protection against unauthorized and fraudulent transactions. Banks end up eating alot of the fraudulent transactions since they can't charge them back in many cases. Banks are not going to eat a transaction because the customer changed their mind. It is between the customer and the third party to resolve the problem.