Why would existence remove my knowledge after reicarnation?

why would nature be so cruel to remove your memories and wisdom reincarnation after reincarnation to make you step on the same stones again?

There is no evidence for "reincarnation". Your question is unrelated to "reality". What you have called "ignorance" (of the Four Noble Truths) and "lust" ("raga") are related to reproductive & survival instincts. This things exists because nature creates 'raga"; which is probably related to the energy of chemical reactions & heat that propel physical creation.

The fact that there is no evidence of wisdom passing from life to life is evidence against reincarnation.

why would nature be so cruel to remove your memories and wisdom reincarnation after reincarnation to make you step on the same stones again?

One of the Noble truths is acknowledging that pain or suffering exists rather than denying it so perhaps nature or reality is naturally cruel.

But it's not really reincarnation rather rebirth or re-existence in one of the five realms (hell, the animal realm, realm of ghosts, humans, devas).

Birth as a human is extremely rare the majority of humans most likely came from hellish worlds, the animal realm, or the realm of ghosts prior to this human existence (as implied in the Pansu suttas SN 56.102-113) and don't naturally automatically remember past existences it's only gained through developing one of the six higher knowledges (pubbe-nivāsanussati).

Christian Gnostics believed that it's because this world is controlled by Satan and only holy knowledge can give you salvation. Is karma (which is a religious belief) the only answer Buddhism has to this matter?

The concept of Satan might have originated in Buddhism as Mara the "Evil One" is a central figure in early Buddhism and pre-Buddhists religions seem to not have any Satan figure only post-Buddhist religions like Christianity and Islam which were obviously influenced by Buddhism since Ashoka sent Buddhist missionaries all around the world.

Kamma is one explanation but it's also explained in the suttas the nature of things is impermanent and subject to change.

Nature is not a personal entity, as far as we know. There are laws of nature, and those laws function independently of any moral or axiological (judgements of value) consideration. Reality is what it is, and it does not care about your evaluation of it. It makes no sense to judge it as "fair" or "unfair", mainly because those are subjective concepts.

Kamma is just one of those laws: any action has its consequences -in the mind and in the external world-, and the most important factor, especially when talking about suffering (and its perpetuation and cessation), is intention. (By the way, 'kamma' just means "action", and it is not necessarily a religious or superstitious concept; it depends on your definition and understanding of it).

Think about this situation: one you were a child, you took a lot of decisions and made a lot of choices, and it is likely that most of those choices were made without major consideration or analysis of the potential consequences. And as a product of those decisions, you experimented some of those unreflected consequences, some of them probably until this very day.

Would you say that it is unfair that you "suffer" the consequences of unreflective deeds made by a child years ago, considering that you are not that child anymore?

Consequences, and laws of nature in general, all happen whether you like it or not, and the wisest thing you can do it to understand and accept those unavoidable laws, and learn how to act according to their influence.

Also bear in mind that "rebirth" (and not "reincarnation", because since there is no permanent self/soul, this latter concept is not part of most buddhist doctrines) is a controvertial topic, whether some buddhist like to accept it or not. So not everyone would agree with the idea of something (consciousness, memories, tendencies, etc.) continuing after biological/clinical death.

Kind regards!

maybe my English is not good enough, but I think your question is possibly based on a misconception. "Rebirth" – not re-incarnation as Brian Diaz Flores clarified – ist not a kind of "reset", so that you start as a blank paper again so that

you step on the same stones again?

Which would make Buddhism indeed very sadistic. Due to applying buddhist teachings in your life you will lay good foundations in your mind, which will bear fruits in next life. In fact this is the aim of all Hinayana-Teachings: Personal liberation due to ethical discipline. It's not like having a "memory" as a mental factor. (Remembering past learnings). It's more like a healthy attitude you are strengthen life after life due to collect "merit". So some stones will vanish. (Hopefully)

why would nature be so cruel

"Cruel" sounds like dukkha -- as if nature were ill-willed and unkind, and we were averse to that.

So I guess that's among the many kinds of view or perception that we should overcome (in order to do away with dukkha), craving things to be other than they are -- though maybe also acknowledge whatever truth there is in it to become dispassionate about whatever is impermanent.

"He abused me, he struck me, he overpowered me, he robbed me." Those who harbor such thoughts do not still their hatred.

to remove your memories and wisdom reincarnation

I suppose you're not supposed to see them as "your" memories and "your" wisdom.

They are memories, perhaps they are wisdom, but they are, "not mine, not me, not my self".

To some extent wisdom isn't removed -- from the world -- by death, in that the Dhamma continues to exist. I think that's similar to the view that there's a dharmakaya.