re: "I have reached out to the client but what is my course of action should they not respond?"
I don't know what actually happened in the original poster's situation.
But if a client wants to ask Upwork to refund manual time, then (as Petra mentioned), Upwork does it and there is no recourse for getting paid for that time.
If a client does that to you, then it probably means it is time for you to stop working for the client. A client who trusts you and you wants to be trusted by you does not go behind your back and ask Upwork to refund manual time.
I have had clients who had concerns about time logged, maybe because there was a problem with communication and they had not expected me to work on something that I worked on... When such clients come to me directly and express their concern, I am very flexible. I can remove hours from the work diary (manual or app-logged), in order to help them out.
But a client going behind my back? I would probably just send them a short "thank you" note, and close the contract myself.
Another possibility: If a client simply had a problem with their payment method... I might be more patient. But I wouldn't be happy about any of my billed time being reversed - even if it WAS manual time. I would hope that the client would resolve any issues with their payment method. But I would certainly not do any more work on the project until they fixed their payment method and also paid me back for the reversed time.
