Etsy will eventually side with your customer, give them a refund, and NOT ask them to return the package. You should NEVER tell customers to file a case on you.
If it was damaged, it doesn't matter how slightly, it is your responsibility to pay for the postage both ways, because the customer did not get an item as it was described. If you want it back, you should print a pre-paid postage label and send her a link to download the label. At least that way, you will get your discounted postage rates, which are probably a lot less than the customer would have to pay to purchase postage, and then you won't have the hassle of having to reimburse her. You can't refund more than she originally paid, so you would then have to figure out how to reimburse her for the return postage if you don't send her a pre-paid label.
In the future if an item is "slightly damaged" in shipment, try offering them a pretty good discount to keep it and fix it themselves. That will be cheaper for you in the long run. If you think you can fix it and resell it when you get it back, it may be worth paying the return postage. If it's not, I ask for pictures of the damage and let them keep it, as part of my apology.
I would never ship anything to a foreign country without insurance. That way, you will be reimbursed for the damaged item, so you won't be out anything. But in that case, I ask them to keep everything, including the packing materials and box for two weeks, in case the carrier wants to see it in person. Usually, pictures are good enough, but not always. If they return it to you, regardless of who pays, that will void your insurance claim, and they won't reimburse you.
Good luck getting any help from Etsy. They have the worst customer service for sellers of any marketplace I know of. Usually, they will take up to 10 days to reply, if they reply at all. Sometimes, they just ignore you.
The first reply or two will probably be a canned response that does not address your problem. They may even say their decision is final, but if you are persistent, you will eventually get a real person to look at it that may help you. That is if you contact them by email from the form they provide and don't open any other threads. If you start a new email inquiry, they will close the one that is open and treat the new email as a new problem, kicking you to the back of the line to start over again.
Chat can only answer questions that are already in the Seller's Handbook, and they don't have authorization to make any decisions on anything, especially if it involves money.
Etsy will answer cases once it is escalated, but they will usually find in the buyer's favor, often before you have even had time to tell them your side of it. If they give the customer their money back, they will not make them return the item, so then you are out both your money and your merchandise. It is always best to try to work it out with your customer yourself, if at all possible.
If the item was damaged in any way, it is "Not As Described" and Etsy will always refund the customer for that reason. If the customer is in one of the EU countries or the UK, you have to give them 30 days to ask for a refund for any reason or no reason at all, and you have to refund the original postage plus pay for the return postage if you want it back, or they can keep the merchandise, too.
