I received from my hosting provider (Softlayer) a trademark claim from a brazillian company because their trademark appears in one of my pages beside another trademark they don't want to be connected anyway.
The content comes from a script wich makes a search on the fly into Youtube and offers video clips related to the search.
The company has a channel in Youtube and they do not disabled the option to give the content to third parties (Youtube T&C 8.1.a) so the usage of the trademark is absolutely correct according the US law (not the brazillian laws they comes with).
Although the claim is simply and plain stupid and just proves how useless overpaid lawyers can be, the issue was assigned to a simple mind employee unable to write something more than "remove the offending content, right now".
How can I explain him there's nothing wrong in this page? Should I change the hosting provider before they cancel my account?
IANAL Potentially, a ruling could mean the site is taken down while it is evaluated in a court of law. That would be the worst situation.
I'd suspect the complainant will follow your hosting - it's the site content they are concerned over. And, why should you have to switch hosts just to display the content. If you did switch, you may have other issues develop, such as serps positioning.
Can you alter the script so that the complainant's channel no longer appears?
I'd ask myself the question if it's worth the hassle of fighting it, no matter how stupid the complaint may be.