Personally I would block the buyer, then I would make sure that blocked buyers couldn't contact me. The buyer's only means of communication after that would be to actually open a case.

If the buyer has a habit of abusing the Money Back Guarantee eBay may have already restricted their ability to use it; that might explain why they're so reluctant to open a case. If they did open a case you would need to ask them what the cost of a return label was (or even better - find out for yourself) and only send an amount that would cover the cost of a return label. If the buyer didn't send the item back they wouldn't have any way to obtain any further funds back from you.

In my opinion their first warning shot was when they asked for a price reduction prior to purchase; especially when "best offer" was already enabled on the listing. @major-d-clutter - what does their "Feedback left for others" look like? Are there any red flags (or rather, red dots) there?

You may not even have a human dealing with a case, just eBay's automated systems including AI.

An eBay human may become involved depending whether, or how far, a case gets escalated, by which point some harrassed anxious sellers have chewed their fingernails to the quick.

You can't provide a label through ebay.

You either find a way to do it outside ebay or send her the equivalent in funds.  She will need to give you her address for you to see the cost.

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@major-d-clutter wrote:

Ebay are telling me to send her a shipping label, This was dealt with through GSP so I don't see how I can provide an US buyer with a shipping label. 

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Ask the buyer for her address; you can then get the cost of a shipping label. For example, you could try UPS here. You can then either purchase the label yourself or send the funds so the buyer can purchase it. Either way I would suggest you take a screenshot of the page showing the cost of the label in case you need it later.

Ideally you want to purchase the label yourself so you can declare the value and indicate it is a "return of goods" on the customs form.

Ebay have refunded the buyer and have told her to keep the mirror. I have lost my money and the mirror. I was told twice by ebay not to worry as they had my back as the mirror had gone through GSP. Now it appears that this is not the case. The left hand doesn't know what the right hand is doing.