This may be set up this way intentionally within your organization so that credits cannot be charged back directly to cards without proper authorization. It could be one way to prevent internal theft as well as a way to make sure charge backs are done with proper authorization.
As there are points lost to each credit card company when running a charge and a credit, you may be set up intentionally this way to have the credit be used as a "store credit" towards a new purchase rather than refunding. You may want to check with your credit manager.

With that said, We currently have to do charge backs in Virtual terminal (done by clerk) and then apply the charge back in A/R (done by Credit Manager or higher overseer of the department) when approved. Otherwise, credits are left on account to be used as 'store credit' towards next order.

Thanks Dean. I have spoken with our CFO and ideally we would like to process credit card refunds like this through Sage. We do not want to leave them as “store credit”.

We are using Sage Exchange and I found this document on processing refunds in Sage 100 through Sage Exchange. It looks like we are taking the right steps but we can’t choose the invoice so we’re stuck.

Is this a setting change inside of Sage? 

I am only a user of SAGE 100ERP and not a SAGE developer, programmer, or SAGE representative.
I will have to leave your question to be answered by someone else on the forum or by your SAGE contact representative.
Sorry.

We don't use Sage Exchange and I didn't read your document.

But I have never had a problem applying a credit memo to a fully paid invoice. So unless someone else pipes in, I suggest scouring through your role settings for something that might be blocking it.

Also, has the data entry screen been modified and the field locked? (I'm guessing not, since I don't see an asterisk.)

Invoice #, Credit Memo, Customer Number. In that order on my ABC system, the apply to invoice field becomes available for some customers and not others. I don't know the distinguishing characteristic required, but perhaps someone else might know.

Balance forward customer perhaps?

After some additional testing and comparing, we found that there were some customers where we could select a previous invoice when doing the Credit Memo but some where we couldn't. When we compared the two types of customers the thing that was consistently different was how invoices were applied to that customer. On the ones that would work with a Credit Memo there would be one invoice # representing the invoice and the payment. When we select that invoice you can see two Transaction Types--one of Invoice and one of Payment. Here's a screenshot of the ones that do work with Credit Memo.

However, on the customers where we could not apply the Credit Memo to a previous invoice there would be one invoice entry with a type of "Invoice" and one with n Invoice Type of "Payment" that was exactly negative amount of the Invoice. Instead of the payment being applied to a particular invoice, it's a separate "Payment" invoice. The additionally confusing thing is that the "Payment" invoice number is completely different than the real invoice number. Here's what I mean:

Another thing we noticed is that the "Payment" invoice ID is shared with some other customers' "Payment" invoices but it's not always the same.

What we can't figure out why is why some orders come through correctly and some do not. Does anyone have insight into what a "Payment" invoice is and what we might be doing wrong to make that instead of it showing up as a Transaction Type of "Payment" under the real invoice?

Did these payments get posted before the invoices?

Your payment ID is just the date, which could explain why it's duplicated across customers.

If you go into cash receipts and match the payment to the invoice so that both are zeroed out, does that fix the problem with being able to apply a credit memo to the invoice?