Icelanders have mitochondrial DNA from a Native American woman.

So notes a recent study.

I'm only noting this, as it's interesting.

Recent evidence suggests that Vikings first colonized North America in 1021.  Of course, they probably showed up prior to that.  But, at any rate, they were showing up in North America by the 1000s.   They were aware of North America, for that matter, in the 900s, so recent studies not withstanding, I'd be surprised if they didn't have some sort of presence, perhaps only occasional and seasonal, in the second half of the 900s.

And at some point, one of them brought a Native American woman home to Iceland.

Now, we don't know the circumstances, and so far it seems to be only one, which is odd.  But it did occur, and she had children, and some of her children's children, carried down many times, live in Iceland today.