If the schedule change is sufficient so as to permit a cancellation and refund, the COC expressly require AA to refund to the CC used to purchase the ticket. If you read the entire lengthy provision relating to refunds (International COC, Rule 90), you will see that the refund provisions are specifically written to prevent value from being paid to anyone other than the purchaser when other than cash is used.
This should not cause any accounting headaches so long as OP advises his client that it will be receiving, as it should, a refund of whatever the amount is. The client will reflect that amount as reducing its cost of doing business, e.g., paying OP's travel and the client is fine.
OP on the other hand is out approx. $100, but can deduct the unreimbursed expenses (presuming that he is a US taxpayer), so he is really only out the $100 less marginal tax rate. Alternatively, he might simply advise the client that it will see the refund and that he will now submit full expenses.
Not to chastise OP, but this is all far from best business practices. Things go wrong all the time. Far better to let the tickets cost what they cost and to expense whatever expenses are.