The following is a very slightly modified version of my previous post in: Did the Vikings ever mix with the Inuit that lived in Greenland?
+++
In short, the surviving evidence suggest that a few of those who belonged to the Thule material culture might have been taken to Iceland by the Norse people, probably not spontaneously, but it would be a very rare event (otherwise the following two most relevant evidence would not have been recorded and transmitted to us).
An alleged 17th century transcript of the 14th century Norwegian captain reports that they caught two Inuit boys in the coast of Greenland, (though I'm not so sure about the authenticity of this account), and another, independent 16th century account (the Description of the Northern peoples (1555)) notes two canoes of Skraelings hanged on the wall of the cathedral of Oslo, taken by the Norwegians from Greenland in course of the 14th century.
While [the majority of] scholars agree that the people with Thule material culture (now Inuits) began to flowed into north-western Greenland in the 13th century and later, and two groups of the people, namely those with the Thule culture and medieval Norse settlers, might had some sort of contact as well, they have not reached an agreement for what the most common characteristics of the relationship between these two groups would have were.
At least one gene test project was in fact conducted in the last decade, but the result is basically negative on the ancient admixture between Inuits and Norse people.
'Although it has been speculated that there has been historical admixture between the Norse Vikings who lived in Greenland for a limited period ∼600–1,000 years ago and the Inuit, we found no evidence supporting this hypothesis. Similarly, we found no evidence supporting a previously hypothesized admixture event between the Inuit in East Greenland and the Dorset people, who lived in Greenland before the Inuit' (Moltke et al. 2015).
While some archaeologists, including at least one leading Danish researcher of this field of research (Hans C. Gulløv) suggest the possibility of co-existence between these 'native' Greenlanders and Norse Greeland settlers, even involving some kind of 'trade' between hunting products and iron (?) allegedly occurred in the hunting grounds in middle-to-northern Greenland up to Buffin-Ellesmere islands, it is neither so easy to contextualize fragmentary Norse finds salvaged from Thule culture sites nor to date various archaeological sites and artifacts that belong to different material culture, even among the 'native' groups of people: In fact, Gulløv proposes the hypothesis that the three types of groups of peoples, namely two 'native', Late Dorset, early Thule, and the Norse Greenlanders were active in northern Greenland about at the same time, in the 13th century (Gulløv 2008), though his dating has been disputed by some researchers.
On the other hand, one latest book on the Norse Greenland settlements by the historian Nedkvitne, focuses on somewhat hostile interaction between Inuit people and the Norse settlers in the latter's last phase, in the late 14th century, attested by the contemporary Icelandic texts like Icelandic Annals (Nedkvitne 2019).
Ethnologists in the 19th century also collected some orally transmitted folktales from the Inuits on their relationship with Kavdlunait (Europeans=Norse settlers before the 'second discovery' of Greenland by the 18th century Danes), but the date of these traditions were so late that I'm personally not so inclined to take their narrative at face value. Anyway, the Inuits seemed not to have forgot all the memory of their old contact by then.
If you are interested more in this topic, I'd recommend to check the comments posted in these threads:
References: