I can answer part of your question right away! I'll leave it to someone else if they want to discuss a more detailed history of the Norse and Inuit interaction, but I can address the fact that your question hinges on the somewhat flawed assumption that the Norse colonizers were interacting with a single established native community that they termed "Skraelings".

There was a indeed group called the Late Dorset Culture that were living on the Northwestern section of Greenland from 800-1300 C.E. and overlapped with the Norse for a couple centuries. These small settlements were the final of a series of independent stretches where the Dorset people of modern day Labrador and Newfoundland had inhabited the island. There is some evidence of trade between them and the Norse as Norse artifacts were found in several Dorset archeological sites (1), however, I have not been able to find much information about the Dorset. When the Norse arrived in the 10th century they colonized the uninhabited Southern tip of the island, so it seems likely that there was limited contact between the two cultures due to the large geographic separation between them.

The term "Skraeling" on the other hand, typically refers to the Thule people (the ancestors of modern day Greenlandic Inuit) who arrived to Greenland 200-300 years after the Norse colonization and coincided with a period of slow decline and abandonment of both Norse and Dorset settlements. I find this nuance particularly interesting because it subverts a lot of our notions of Europeans being inherently the "big bad colonizers". In this case a non-European pre iron civilization was able to show up and push out the Norse of all people, which is honestly pretty badass. While archeology seems to indicate that the majority of the settlements were abandoned peacefully due to reasons such as a cooling climate and the decline in demand for Greenlandic Ivory, evidence such as the record below indicates that the Norse were not faring well against the new arrivals.

"Pope Nicholas V prescribes the Bishops of Skálholt and Hólar to ensure to provide the inhabitants of Greenland priests and a bishop, which of the latter they haven't had in the 30 years since the coming of the heathens when most churches were destroyed and the inhabitants taken away as prisoners."

Overall I just wanted to clarify the slight misconception of "Skraelings" vs the native Dorset Culture and point out a fun tidbit. I invite someone else to please add more about Norse and Inuit relations.

(Also for the record I am not trying to undermine the Inuit's claim to Greenland in any way or claim that the Norse are the true natives. I just think it's a neat example of the "Vikings" getting their butts whooped)

(1) Greenland Research Centre at the National Museum of Denmark. Retrieved September 3, 2008.

(2) D'Andrea WJ, Huang Y, Fritz SC, Anderson NJ. Abrupt Holocene climate change as an important factor for human migration in West Greenland. Proc Natl Acad Sci U S A. 2011;108(24):9765-9769. doi:10.1073/pnas.1101708108

You might also find it interesting in what /u/Kelpie-Cat and I wrote recently on the Thule culture in: Multiple Questions Regarding the Thule Culture.

(Added): As for the relationship between the late Dorset people and the Norse settlers in Greenland in the earlier phase, what I answered in this previous thread might also be useful: Did the Vikings ever mix with the Inuit that lived in Greenland?.