We know that the sagas of the Vikings mention the native Americans but is that true the other way around? Are there any native American stories about the Vikings?
While it's clearly better to wait for the more definitive answer from the specialist in native American history or folklore, I'll post a very brief note as well as a link on the supposed nature of the relationship between the Norsemen and the Native Americans.
As I wrote my post in the question thread, Were any diseases brought to America by the Vikings?, there was next to almost no trace of the direct contact between these two groups except for the notices in the sagas. So, it is rather natural to surmise that no oral tradition of the native Americans focus on their encounter with the Norsemen (the contact was extremely limited, and the sagas was at least written in the parchment ca. two centuries after the incident).
On the other hand, the Norsemen used the same term skraeling to denote the 'other' groups of people of Vinland, Helluland (the Buffin Island?), Markland (Labrador), and Greenland, where their settlement had lasted for ca. four centuries. While I myself is skeptical of any historical value (since it had been recorded ca. five centuries after the demise of Norse Greenland and even more than one century after the re-discovery of Greenland of the Danes), Danish geologist Hinrich Johannes Rink (d. 1893) collected the legends and tales among the Inuits in Western and Southern Greenland in later 19th century.
Some of the tales Rink collected indeed narate diverse relationships between the new-comer Inuits and the ancient Kavdlunait (Europeans, i.e. medieval Norse settlers) in Greenland. Rink's folklore collection of the Inuits are now copyright free (1st edition had been published in 1875) and easy to find across the Internet, like Google E-Book. If you are interested in such traditions, please check '54: Stories about the ancient Kavdlunait' and '55: Pisagsak and the Kivigtok' (Rink 1875: 313-24).
References:
[Edited]: fixes typo.
The Kalaallit (Greenland Inuit) have several stories concerning the old Kavdlunait / Qavdlunait - their word for Europeans - that came before the modern Danish arrived. I summarize a few of them in this post.
As for Native Americans proper, unfortunately the Beothuk, the people most likely to have had direct contact with the Vinland expeditions, did not survive later colonization. So we don't know what stories they would have told about the events.
I've answered a similar question on the subject before. The last few paragraphs should answer yours as well. :)