Need legal advice: New business owner asking me to remove a past personal project

A year and a half ago, I did a personal project where I created beer bottle packaging and branding for a fictitious brewing company called Bottle Rocket Brewing. You can see the project on my site here: http://ift.tt/1M7yFqe

Today I got an email from somebody who is starting an actual Bottle Rocket Brewing company in another state and they requested that I remove the project from my website. This is their site/logo: http://ift.tt/1yfB5HB

I'm arguing that it's a personal project and I'm not profiting from sales of the design in any way, nor am I using their actual logo (because I created my designs before they created theirs.) They still are insisting I remove it and claim that I'm profiting from their company name.

Am I legally obligated to remove the project or can I safely ignore it?