Yes, it can be shocking to come across the term “hostile/hostilely” in this context, and yes, it does actually mean “de manera hostil”, in the sense of “without permission or authorization”, which is, I concede, also a form of “hostility”, at least to a certain degree.

This expression is related to the so-called “adverse possession”, which is described below in detail:

See reference below:
https://www.nolo.com/legal-encyclopedia/what-open-notorious-...
What "Open and Notorious" Use of Property Means for an Adverse Possession Claim
(…)
An important element of establishing a claim to another person's land using the legal doctrine of adverse possession is that trespassers must be "open and notorious" in their use the disputed land. That's on top of the other requirements that the use be hostile, actual, exclusive, and continuous for a certain number of years (usually set by state statute).
(…)
Now consider whether this matches the elements of adverse possession: Bob can establish that his use of the pond was hostile (without his neighbor's permission), continuous for the statutory period (30 years is far more than most states' laws require), and exclusive (assuming no one else took part in his moonlit swims or otherwise used the pond).

Situation in the Spanish speaking countries (= posesión adversa):

https://estudyando.com/que-es-la-posesion-adversa-definicion...
¿Qué es la posesión adversa? – Definición, ley y casos
(…)
Requisitos para la posesión adversa
La posesión adversa requiere que una ocupación sea:
1. Hostil
2. Real
3. Abierto y notorio
4. Exclusivo y continuo


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Note added at 1 hr (2021-10-06 18:53:05 GMT)
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Diego, I understand you are Artgentinean. In such case, you will then have to verify if my rendering is also applicable in your country, I think it is, but I am not sure, and you did not mention the target countty.

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Note added at 1 hr (2021-10-06 18:56:53 GMT)
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Please, excuse my typos: "Argentinean", "country" was the intended spelling.

By the way, Argentineans, Argetinians, Argentines... ??? Uf, heeeelp!

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Note added at 1 hr (2021-10-06 19:00:55 GMT)
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Thanks, Diego. I think "hostil" is fine then.

Thanks, Diego, still so much to learn from our colleagues from the other side of the pond. So "Argies " too, really? Okay, noted with thanks.

You live and learn...