Not really sure how to proceed- Damaged item with reshipper address

[jdkusanagi]

So, even though I've been using eBay for a while, I don't sell too often. COVID and being laid off kinda forced me to start.
Anyways, I had shipped an item out on June 16 to a US address. The item arrived on June 22 and was marked as delivered.

5 days later, the buyer claimed that it arrived damaged. They did send pictures, but the first couple looked like the item was undamaged, and the last 2 looked like the item was damaged (or has removable parts). They requested a partial refund and stated that he could fix it with glue.

I responded by stating that I apologize for the mishap and would be willing to do a partial refund. There was no answer for 2 days. So I sent a follow up message and asked if the amount was still alright.

No response again, but for 7 days. Today, they responded simply by saying they wanted more refunded than was offered. 

I looked up the address and it seems the address I had shipped it to was a reshipping company address.

In doing some searches, it appears that if I do ask them to just return the item instead for a full refund, I'm only responsible for the shipping label from that address and not anywhere else they shipped it to.

Now, should I not do anything until they file a claim with eBay? And also, if they send it back and it was already glued/altered, then does it warrant the full refund? 

I have pictures before it was sent with my ebay id on a paper with it and a timestamp and they match the condition of the first 2 pictures that look undamaged. 

I'm not clear on how to proceed. I called eBay and they pretty much just stated that because the buyer did not open a claim yet, it's up to me how to go forward. Because the item is not really cheap, it's not one I can just refund and let go. Advice?

[marnotom!]

Items where the buyer has arranged shipping or where they’re handled by forwarding agents are generally not covered by eBay’s Money Back Guarantee or Buyer Protection programmes.

It was very generous of you to offer a partial refund but there was no “business reason” for you to do this, as the damage could well have occurred on the forwarding agent’s watch, after your responsibility for the item’s safe passage had ended.

Seems to me at this point the ball is in the buyer’s court. You’ve communicated plenty with this buyer. Where did your item end up going after it reached its US destination?

[jdkusanagi]

This was not disclosed by the buyer, but some research indicates strongly that the item was shipped to Korea. 

I offered the partial refund, but before searching the address (which really I should have before replying the first time- lesson learned). I did deny the second request for more money- but asked for more information and indicated that the first pictures were pictures that looked like the item was undamaged and the last pics were damaged after unboxing. 

My assumption is their reply may again take a while as it's maybe getting forwarded through the shipping agent.

[marnotom!]

I’d also do some checking on how the forwarding agent deals with damage claims, if at all.