I should just offer a return/refund, correct?

Long story short...the buyer messaged me to send their item to a different address after they bought it and I did agree (I know you shouldn't do this now).

Anyway, I accidentally sent the item to the address the have listed on their Paypal/Ebay instead of the one they asked me to. They then shipped it from the address I did ship it to to their current address.

They then messaged me that they wanted a refund because they bought the jacket for a trip and didn't get it in time because I didn't ship it to the correct address.

While the ad does state no returns, I should just admit it was my mistake and offer a return/refund, correct?