Two things we need to establish here. First, did Native Americans have scientific knowledge, and second, did that impact European science?

To the first point, it would be easy to say that Native Americans had no scientists since they never employed anything like modern scientific methodology, but I think that answer is a little too flippant and dismissive. Instead, I like how you phrased it as "scientific knowledge". Phrasing it that way is more product oriented rather than method oriented, and we could argue that anyone that produces "scientific knowledge" is a scientist, regardless of the methodology they follow. We could argue that "scientific knowledge" is any knowledge about the natural world gained empirically.

This is close to the argument anthropologist Bronislaw Malinowski makes in his seminal (though very dated) work, Magic, Science, and Religion from 1948, emphasis mine (page 1):

There are no peoples however primitive without religion and magic. Nor are there, it must be added at once, any savage races lacking either in the scientific attitude or in science, though this lack has been frequently attributed to them... ...On the other hand, a moment's reflection is sufficient to show that no art or craft however primitive could have been invented or maintained, no organized form of hunting, fishing, tilling, or search for food could be carried out without the careful observation of natural process and a firm belief in its regularity, without the power of reasoning and without confidence in the power of reason; that is, without the rudiments of science.

To break it down, Malinowski makes the argument that science relies on three things:

1. observation of natural processes

2. belief in the regularity of nature (or natural processes)

3. confidence in the power of reason to understand these processes

The result of these three is the production of scientific knowledge, i.e. knowledge about the natural world. Malinowski makes a similar argument about magic, with the important difference that magic relies on careful observation and belief in the regularity of the supernatural, rather than the natural.

If we follow from this argument, and as Malinowski states, all societies then produce scientific knowledge in the sense that they rationally accumulate knowledge about the natural world through empirical observation. Richard Nelson in his easy to read article on Eskimo Science makes the case that the only fundamental difference between this kind of science and modern scientific practice is that the invention of scientific methodology has significantly increased the speed at which society can accumulate this kind of knowledge (over the course of a years or decades, rather than at the rate of generations). For instance, he argues that the scientific knowledge he witnessed working with Inupiaq hunters - such as the ability to predict where whales will breach on the surface of the ocean - could be replicated by modern biologists in a few months of systematic observation, but also argues that the same results were ultimately arrived at by generations of hunters carefully observing the natural world around them in the course of their daily lives.

You can of course make other arguments about how science requires scientific methodology, but I don't find that perspective helpful for answering your question so I will stick to the line of argument made by Malinowski and Nelson.

To that end, Native American scientific knowledge was very impactful for European naturalists trying to document the new environments they found themselves in due to European colonialism. While not always the case, whether scientists or not, Europeans arriving in new environments in the Americas tended to rely on local people for knowledge about these environments. In the Southwest, the area I know best, the knowledge necessary to successfully farm and gather resources in an arid environment was crucial to colonizing Spaniards in order for them to successfully feed themselves outside of just taking food from native people.

In a broader social context, we can consider the various New World domesticates (plants particularly) as results of scientific knowledge, and these products (particularly corn and potatoes) are of course incredibly impactful on societies across the planet. Botanical knowledge is one area that has been consistently utilized by Europeans in contact with Native people. The use of tobacco, for instance, is the result of Native knowledge about the properties of the plant.

This is an ongoing process, and the field of "Traditional Ecological Knowledge" is an hot area for study in modern anthropology. Concern has been voiced, for instance, about the use of TEK by pharmaceutical companies and what obligation they have to reimburse communities from which they obtained knowledge about certain medicinal plants and to what extent that knowledge can be considered intellectual property.

All that is to say that while Native American scientific knowledge may not have been particularly influential on European science, to the extent that scientific knowledge is useful to a society (either directly, as in farming techniques, or indirectly in the products of that knowledge such as corn or potatoes) Native American science was made ready use of by European colonists throughout the Americas.

Edit: Typos.

This is an interesting question since we are really dealing with two pre-modern societies in which our concept of “science (fuck yeah!)” does not really exist. There’s often a tendency to anachronistically conflate several centuries of European history, in relation to the Americas, into some sort of blend of everything from the 16th century into the early 20th. If we look at the some of the earliest interaction between Europeans and Americans, that of the Spanish and Mesoamericans, what we really see are Europeans who are really still a medieval society, and one that often saw more in common than in contrast with the new peoples with whom that were interacting.

Preface aside, one of the clearest example I can think of is in the field of the natural sciences. With a whole new continent of flora and fauna, Europeans often leaned heavily on the people who for whom these plants and animals were banal to help make sense of them. To further narrow down, your question immediately made me think of the works of Francisco Hernández, the Spanish Court Physician who spent several years in Mexico traveling about to catalogue the medical and herbological knowledge of the region. His works are instructive in a number of facets, in that it both shows the incredible depth of knowledge he was encountering, but also shows his own biases, wherein he will sometimes discount an indigenous classification or use of a material based upon his own medical worldview, which, again, was a strictly pre-modern and rooted in humoral theories.

Ortiz de Montellano, in Aztec Health, Medicine, and Nutrition, actually uses instances of Hernández disagreeing with the titici (physicians) from whom he was learning as counter-examples for syncretism of European and Mesoamerican medical theories. As noted before, Hernández was trained in the humoral tradition rooted in Hippocratic and Galenic concepts of the body and classification of the natural world into items with “hot,” “cold,” “wet,” and “dry” properties. Similarly, we see in the earliest works on Nahua medicine (Sahagun, Badianus), a distinction between “hot” and “cold” items, which have led some to advance a rapid adoption of Galenic concepts into Mesoamerica. Ortiz de Montellano instead argues for a pre-existing dichotomy which slipped into the writings under the terms of Galenic medical discourse, writing:

Hernández’s training in the Galenic theory of humors and of curing by correcting humoral imbalances prevented him from understanding Aztec etiologic concepts different from his own. For example:

[achilto] They say that the sap put into the nose cures headaches, which seems senseless since its nature is cold and glutinous unless the pain is due to a hot cause.

However, the Aztecs believed that headaches were caused by excess blood in the head and cured by its removal, rather than due to an imbalance of hot and cold, a Galenic concept that Hernández could not abandon.

Likewise, Ortiz de Montellano points to instances where the Galenic and Mesoamerican classification of the properties of medicinal plants stand in contrast as evidence of an indigenous dichotomy, such as with remedies for coacihuitzli (gout). Seen as “cold” disease, all of the Aztec remedies are classified as “hot.” Hernández, on the other hand, classifies some remedies as hot and some as cold, saying:

The leaves have no taste (therefore classified as cold), but nevertheless the Indians say that applied locally they cure pains.

Similarly, we can see Hernández’s blind spot for non-Galenic knowledge when he criticizes the titici for never practicing venesection, or allowing women who have recently given birth to use temazcalli (steam baths). This is what I meant earlier by noting that the Europeans were a pre-modern society, and thus referring to their “science” represents an anachronism. Hernández disparages Mesoamerican practices not because of any empirical, rigorous testing, but because they contradict his own folk traditions.

Nevertheless, this did not stop Hernández from spending the better part of decade cataloguing the medical and herbal knowledge of the region (if sometimes only to quip on how poorly it was utilized). Particularly noteworthy to the Spanish were those plants which could cure the “French Disease,” that is, the new plague that had been ravaging through Europe starting in 1495, which we now call syphilis.

References to remedies for syphilis are numerous throughout Hernández’s works, but I find one in particular to be noteworthy, which is the passage on hoayacan (which he notes is also called guayacan):

It’s effects are used to cure the French malady and chronic diseases of the head, chest, stomach, gall bladder, kidneys, and pains in other parts of the body. The method of cure is a remedy that, according to my way of thinking, should be known to all who practice medicine.

Hernándezd oes not go on to describe this method, in part because it should be obvious, you unlettered buffoon, but also because he was describing guiacum, or lignam vitae, which had begun to gain preeminence as a cure for syphilis in Europe. Now, guiacum does excatly nothing to help with syphilis, but other items catalogued by Hernández have lived up to their hype. One that I’ll mention here is ahuacaquahuitl, whose:

seeds have the taste of bitter almonds, and produce, when they are pressed, an oil similar to that of almonds not only in aroma but also in taste and with respect to other properties. The oil cures itching and scars and is also good for those suffering from dysentery, for which it offers some astringency; and it keeps hair from breaking.

Ahuacaquahuitl is actually a tree which should be familiar to English speakers, as it has come into that language as “avocado,” and it is still serving its purpose in strengthening hair and soothing the skin, if its ubiquity in beauty products is to be believed. Cosmetics rarely receive a JAMA review though, but Ortiz de Montellano (1975) did conduct a chemical analysis of several different Nahua remedies and found that chemicals within avocado would “act as antibiotics against gram-negative bacteria. They would be effective emollients against scars and sores.”

We could continue going through the (multi-volume, written in Latin, multiple abridged and heavily edited versions produced over the centuries) works of Hernández, but the larger point is that, when faced with literal continents worth of new material for the natural sciences, Europeans necessarily drew upon the pre-existing schema of those indigenous people who had been exploring, experimenting, and utilizing those products for millennia. While the process of Europeans learning about the New (to them) World was certainly one which took generations and centuries, and had highly variable levels of interplay between natives and new arrivals, such a process would have been astoundingly retarded had Europeans not had ready made sources of knowledge of the natural world and its pharmacopoeia to draw upon in the form of indigenous physicians, wise-men/women, elders, and the like.