Ebay refused but PayPal refund to the buyer

The buyer opened a claim but Ebay found on my favour. The buyer then went to PayPal for help, they refund to the buyer. How can I get my Ebay's payment fee back?

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I always get confused in cases like this. 

 

The sale was conducted on ebay. 

 

The payment was made using eBay checkout which is linked to PayPal. 

 

Pay Pal only process the payment on behalf of eBay. 

 

They are classed as a third party. 

 

So how can PayPal issue a refund if the seller has had a case opened against him by a purchaser and the auction website has decided in the seller's favour. 

 

What information have PayPal been given in respect of this dispute. 

 

Surely Communication between eBay and the buyer and seller are covered under data protection laws

 

To say that eBay and PayPal are not linked as companies just does not seem true.