> I originally had my tagline as "The Free open-source [Company A] Alternative," which they claimed was illegally driving their traffic to my site.

In the UK it’s common for supermarkets to advertise “we price match Aldi”. (Aldi is the trademarked name of a low price supermarket chain). Maybe the US trademark law is different, but I’d be surprised if you can’t claim to be someone’s competitor.

It also occurs that even if their were laws in the US that said that you couldn’t advertise that you were a competitor of a trademark, they’d probably be unconstitutional.