I am not a/your lawyer; this is not legal advice.
I believe the intent, at least, of the Amex Card Member Agreement you mentioned in a comment would not permit refunding a returned purchase to a different credit-card (or for cash). Further, were you to manage to do this, they would be within their rights to cancel any cash back you may have been credited with.
First, we have the following clause from the above agreement:
If permitted by the merchant, you may return to the merchant goods or services
obtained using your account and receive a credit to your account.
As an essentially disinterested third-party, I read this as meaning that receiving a credit to your account (the one used for the original purchase) is a necessary part ("and receive") of the returns process.
A little further on, obtaining a cash refund is explicitly prohibited:
- return goods or services obtained using your account for a cash refund,
The reason behind this clause is probably more to prevent avoidance of the fees or higher interest rates of a cash advance, but the effect is the same: you cannot get cash for a returned purchase.
(Incidentally, were I an Amex lawyer, I would probably try and argue that a refund to a debit card would effectively count as a "cash refund". However, because debit cards are not explicitly mentioned, that argument may not work).
Next, we have:
- obtain a credit to your account except by way of a refund for goods or
services previously purchased on your account,
This clause explicitly prevents an Amex card from being the "other card" in the scenario you are asking about. In other words, if you bought something on a different credit-card (and got points from that card's cash-back scheme), you would not be permitted to return the item and have the amount credited to your Amex card.
In summary, my reading is that refunds of purchases to your Amex card should be made to the original card (where they will cancel/reduce cash-back rewards). Refunds in cash or from purchases made on other cards are explicitly prohibited.
Whether attempting (or succeeding) in getting a refund "that they don't know about" (so as to not lose the cash-back) counts as fraud, or "just" a breach of their terms and conditions I don't know. However, the above agreement contains, in relation to the cash-back program:
We may disqualify you from participating, or terminate your participation in the cash back program at our sole option and discretion at any time with or without cause and without giving you notice
So if they ever find out (or even suspect) that you have "abused the system", they could cancel your participation.