I wouldn't take a chisel to it -- that's for really experienced wood workers.
I'd start with sandpaper -- something in the 200 grit range to get the finish off (which may take care of the problem), and then something around 100 or 150 to sand the wood.
Actually, I'd rout it, but I know what I'm doing....
It's actually not that uncommon. There are variances in manufacturing, and you likely came up with two pieces at opposite ends of the allowed variances.
Of course, I don't see anywhere in my post that says it'll actually work...