Well, 'Inuit' is generally the preferred term but not every group is in agreement on that. 'Eskimo' can be used to refer to all people speaking an Eskimo–Aleut language, in which case all Inuits are Eskimos but not all Eskimos are Inuit (e.g. the Yupik). We can sidestep that entirely here since Greenlanders prefer to be called Greenlanders.

Greenland has been inhabited for millennia, but was settled by the Dorset Culture at the time the first Norsemen arrived. The Dorset were later replaced or subsumed by the Thule Culture, who are the ancestors of today's Greenlanders. (no evidence of assimilation, but no evidence of warfare either) The farthest northwest Norse settlements were around Upernavik (not a Norse name even though it ends in -vik) about halfway up the west coast of Greenland, and that's around where the initial contact would've been made with the Thules moving in from the west. Most of the evidence here is archaeological because we're dealing with one culture that had no written records and another that had very few during the period. The last preserved written record of contact with Greenland is in 1410. The settlements and European contact must have continued for at least half a century after that though, as a hood found in a grave in Herjolfsnes is of a Burgundian style dating from the 1450s.

Around 1200, there is the first reference in the Norwegian chronicle Historia Norwegiæ. Here's a translation; the relevant part is short:

This country [Greenland], which was discovered, settled and confirmed in the universal faith by Icelanders, is the western boundary of Europe, almost touching the African islands where the waters of ocean flood in. Beyond the Greenlanders some manikins have been found by hunters, who call them Skrælings. Weapon wounds inflicted on them from which they will survive grow white without bleeding, but if they are mortal the blood hardly ceases flowing. But they lack iron completely: they use whales’ teeth for missiles, sharp stones for knives.

Since it refers to earlier periods, the people described here may have been Dorset, we can't know for certain, but there's evidence of Dorset contacts. The term skrælling is derogatory (literally means 'weaklings'). But it's not necessarily reflective of an opinion of the Greelanders specifically, because the term had been used earlier for the presumably-Algonquin people they'd encountered in Vinland (Newfoundland). Either it'd become a term for all native Americans, or the author of the H.N. conflated the peoples. In any case, the depiction doesn't lead one to think relations were entirely peaceful.

But peaceful contacts existed, possibly even trade. even cohabitation of some places has been raised as a possibility In the 12th and 13th centuries the Inugsuk culture developed out of the Thule. This culture had Scandinavian influences, in that they used iron for harpoon-tips, they also learned coopering (barrrel-making) and also carved spoons in imitation of Scandinavian metal ones. One of the most fascinating discoveries is a 13th century carving of a European priest in robes with a crucifix, found as far away as Baffin Island in 1978. (Scandinavians might've made it over there too)

A lot of Norse artifacts have been found in Greenlander settlements, which might be an indication of trade. But probably not, as besides the iron, they all tend to lack any direct practical use - e.g. random bits of wool cloth, chess pieces, a church bell fragment. Some of these may have been taken as souvenirs when scavenging iron from abandoned Norse sites. Trade still seems likely, given that the Scandinavians had something the Greenlanders wanted and had in short supply - iron, while the Greenlanders had something the Scandinavians both prized themselves and traded to other Europeans, namely walrus ivory. The Lewis Chessmen are a well-known Scandinavian walrus ivory export of the era, while the beautiful crosier of Greenland's Bishop Smyril (buried 1209) was a domestic use. Even after the 15th century the Inuit would continue to scavenge iron from the Cape York meteorite for centuries.

In the mid 13th century a letter from an Icelandic priest Haldor summarizes several trips north to find Skrælings, but only finding abandoned settlements. It's not entirely clear why they were looking for Skrælings, but trade's a possibility.

Not so much is known about the west-coast settlements, the largest "The western settlement" (Vestribyggð) was abandoned by the mid-14th century; Ivar Bårdsson, writing in 1347 (Old Norse):

The Western Settlement is all Skrælings now. There are many horses, goats, cows and sheep, all feral, and no men, neither christians nor heathens.

The next written record is from 1379 when an Icelandic chronicle reports an attack by the Skrælings, unknown where exactly, where 18 Scandinavians were killed and two taken as slaves. The settlements were in steep decline at that point; the west abandoned, the last resident bishop had died the year before. The eastern settlements still persisted for upwards of a century after that, but this account is reason it was once believed that attacks like this was the main reason for the abandonment of Greenland. Today, the end of the Medieval Warm Period and increase in sea ice is regarded as a greater suspect.

A couple of East Norse words made their way into the Thule vocabulary, and that too bears witness of influence. Although some consider the influence to have been exaggerated (e.g. Palle Koch in Grønland ), what's more certain is that there was essentially no influence in the opposite direction. The Norsemen that we have on record were not interested in learning things from heathen Skrælings. Which is not to say they weren't susceptible to foreign influences, they just had to come from the east; from Scandinavia or Continental Europe. (again: Burgundian fashion) However, one theory of the final fate of the disappearing colonists is that they assimilated into the Greenlander population under the pressure of climate change (and perhaps attacks, piracy, disease, or all those things). They may not have left the location, just their previous way of life.

Additional sources:

HC Gulløv et al, Grønlands forhistorie (Danish)

Fin Gad, Hovedtræk af Grønlands historie, tiden intil 1480 (Danish)

Frode Omdahl, Spor etter det norrøne Grønland (Norwegian)

In English, Patricia Sutherland (whose work is linked in several cases above) is perhaps the biggest name in the Greenlandic and Norse archaeology in the Arctic. So reading her bibliography isn't the worst place to start either.

There's lots to do in this field, many known sites in Greenland have not been excavated. I would expect to find new revelations about this subject in our lifetimes.