Has anyone come across Brandmonitor and how to deal with them?

Question

Law in IT

I don’t even know how to formulate it correctly
After moving from a foreign hoster to a domestic one, complaints began to come to the hoster from Brandmonitor.
According to the hoster, they can suspend the provision of the service if they receive a legal claim.
The trademark they hit on is GoPro.
The product was purchased officially, now it is not for sale in the store, there is just a page marked archive.
Previously, when the host was foreign, they sent complaints directly to the store and they were officially given an answer, although they ignored it.
Actually a question and on the basis of what articles the hoster bears responsibility?
And why blocking can occur even before the court decision, because as far as I understand
before a lawsuit, this is just a letter demanding to eliminate violations, does this mean that they exist (violations)?