I have just been contacted by a company in the US claiming that I have infringed their trademark due to having the same name as them. I am selling products that relieve pain and they are selling therapy services to relieve pain. They wish that I stop using the name and seise all business in the US. They also claim that we are in the same industry and that their customers will get confused and think that I am them even though I have a completely different logo and am not selling services.
The issue is though that they only have a trademark in the US and not in Denmark (the country where I am located in) so is their claim even valid?