Proper Accounting for Erroneous Funds Received

The correct accounting would be a debit to cash and a credit to Unearned Revenue. You shouldn't use AR because this is not a sale on account. When you issue your check as reimbursement, simply reverse this entry.

For security reasons, rejecting the original payment is a safer approach. Otherwise, you may inadvertently be a money laundering accomplice or take part in the Nigerian check scam (if your bank controls are not airtight - payee positive pay, etc.). From the 'books' point of view, it becomes a bank reconciliation timing issue rather than a receipt followed by a payment.

I agree with David, and along those lines, if it is too late to reject the payment, insist on making your payment back to the original payer, not the company it was destined for. In that case, you would need to park the credit somewhere on your B/S, and I would use a non-trade payable account, not unearned revenue.

I agree with all but the most simple method of handling since you stated you already deposited the funds is to reverse it as Marjorie mentions. Whatever GL account you applied the funds to, when you cut a check back to the original check holder you would apply it to the same place. It is then a wash.