A return of money that won't be counted against an order's balance

Solution 1:

Compensation is used in British English to indicate this, for example as a component of the refund paid by banks for mis-selling some financial products.

Dictionary.com: the act or state of compensating, as by rewarding someone for service or by making up for someone's loss, damage, or injury by giving the injured party an appropriate benefit.

Solution 2:

I would call it a courtesy refund, in the same sense as a "courtesy car" or a "courtesy phone": something that is supplied to help out a customer and ensure their continued goodwill. From the OED:

(Supplied, esp. for use) free of charge, as a courtesy: esp. courtesy car. Chiefly U.S.

"He tries to read a courtesy copy of Time, but can't concentrate."

"We've just learned that your courtesy basket was not delivered in time."

"The management provides a courtesy car to the Loop, daily from 8 am to 4 pm."

"In-bound passengers..can wait comfortably in a ‘buffer lounge’ (with pay phones and courtesy phones for car-hire and hotel bookings)."

Solution 3:

Gratuity

Something given without claim or demand. (Dictionary.com)

This is the description you used in your question and the purpose of such a refund seemed quickly understandable.

Another variant in this vein could be gratis, the Latin root.

Gratuity/Gratuitous Refund

Gratis Refund

Solution 4:

I agree with @CharlE that Compensation (or even just Comp) denotes a gift granted by choice of the business owner, generally based on some specific previous transaction, either from gratitude or to make up for an error.

I suggest the other item could be a Refund for Overpayment. This is more like what I think of as an actual "refund", since this is money the customer is legitimately owed because they sent too much money, rather than an optional payment granted by the business.

Solution 5:

For an option that’s perhaps a bit more neutral and that perhaps more vaguely admits that a mistake has occurred, you could consider “offset or offsetting,” which in spite of its neutral/vague nature, still denotes that compensation is being made for something.

offset n.
1. An agent, element, or thing that balances, counteracts, or compensates for something else.
….
offset, offsetting, offsets v.tr.
1. To counterbalance, counteract, or compensate for:
‘ fringe benefits designed to offset low salaries.’

(from ‘The American Heritage Dictionary’)

To the extent that an appropriate adjective to describe the opposite of “offsetting refund/refund (offsetting)” would be difficult to find and/or confusing without (overly) thorough coverage in your documentation (“balancing refund” comes to mind, but it would probably only work for refunds bringing the balance to zero), you could also consider “awarded refunds/refunds (awarded)” or "afforded refunds/refunds (afforded)" for the optional refunds and “entitled refunds/refunds (entitled)” for the required ones.

(all linked example usages from 'Google Books')

afford verb
2. to give, yield, or supply
"the meeting afforded much useful information"

award verb (transitive)
1. to give (something due), esp as a reward for merit: ‘to award prizes’
2. (law) to declare to be entitled, as by decision of a court of law or an arbitrator

entitled adjective
2. having the right or permission to do something:
"You are entitled to a refund.", "

(all from 'Collins English Dictionary')