Re: Does ebay approving a return on your behalf, does that hurt your metrics?
It causes your return rate to rise. It's not one of the metrics they use to calculate your seller level but your return rate is shown in your seller dashboard. Also starting soon (not sure when), if you have a return rate higher than the average return rate in your category/categories you'll have to pay an extra 3% in final value fees.
Re: Does ebay approving a return on your behalf, does that hurt your metrics?
if the buyer wants to return an ietm, making it as smooth as possible is easier for everyone. I set up my accounts that have some returns so that all returns are handled by ebay. I log in and refund when ebay notifies me a return is delivered.
Does ebay approving a return on your behalf, does that hurt your metrics? 
