lol couldn't possibly be worse advice in this thread. 100% do not listen to this and NEVER refund the transfer
FDSGSG is absolutely correct. He should have immediately processed a refund on the $600 as soon as he saw the transaction. By not doing so he risked getting a chargeback and loosing not only the $600 but an additional $10 PayPal chargeback fee.
There is no risk of OP loosing $1,200 to two refunds if he went through the proper refund procedure. A transfer can only ever be refunded once.
Why not?
The only way I see this going wrong is if instead of doing a refund you create a new transfer to send the money back, but you obviously shouldn't do that.
This is merchant 101: always refund suspicious payments before your payment processor has to do it, it'd be really bizarre if Paypal was somehow the only exception in the industry.