An Unnamed register selling domains puts the domain in your shopping basket as a premium domain. So lets say I searching for domains on this registers site and being distracted by tv go to checkout and don't realize a premium domain is in my cart. Yes I click through to fast to look and thinking I have just 4 .coms and as i hit the checkout see the $400.00 for the premium domain. So I pick the phone up and call them but they say no refunds. If it was selling through their auction they could but its from someone else so they can't. So i am like wouldn't i go to an auction site for these. Its not available, its taken and for auction. The 5 day grace period doesn't even apply...The 10 minute refund much less 3 days doesn't apply. How can they legally do this and not offer some refund policy. Even a 1 hour refund policy... Very frustrating.
Typically, the correct thing to do is look at the total amount in your cart before completing the purchase. At the biggest registrar, when you pick a premium domain, they say so. Nothing hidden, not even the cost. I know because every now and then, I pick one. If I don't want it, I delete it before checking out.
I'd inform the registrar that you plan to report their practices to ICANN and see what their reaction is. Don't make it short. Read whom they are. Let them know you plan to be a serious pain for them. Get your money back. If you want, you can still report them. Which registrar is doing this? I'm sure other members here would like to know.
You will need to check the T&C's of the site and see if you can find anything that might help. However to be honest sounds like you are stuck with it.