Your host isn't likely to care unless it causes them grief. There are so many scans happening at any given moment I doubt any of the targets will notice yours.

I do vaguely remember one of these, "I scanned the whole internet! It's easy!" stories from years ago where the author wound up receiving an email from someone at Electric Boat who told them, "Please don't portscan us. We're required to call the FBI when it happens." Your host would probably be "very annoyed" if they received one of those, but I doubt anyone cares enough to send such a message nowadays.