I heard this yesterday during a news interview on a local television station.

Problem:
The adverb “back” makes the statement self-negating.

Explanation:
To “credit” an amount to someone is to refund what that person had paid.

The “re” in “refund” means back. Therefore, one could argue that a “refund back” action would never reach the intended recipient.

In other words, the adverb “back” should NOT be used to modify the verb “credit”.

For fun, I searched Google for “credit back” (with the quotation marks). Unfortunately, I could not use the results to get a reliable estimate of the number of erroneous instances because there are many instances on the Web of correct use.

For example, “Colorado lawmakers want to bring tax credit back.” is an example of correct use of “back” after “credit” because “back” in this sentence is modifying the verb “bring” instead of the noun “credit”.

Solutions:
“They credited me the whole amount.”
OR
“They credited the whole amount to me.”