You would just have to contact the website owner and inform them of the company’s new website. I’d imagine most would be happy to link to it, especially considering it didn’t exist before. But there’s no plugin that can control links on other people’s websites, if that’s what you were asking?
I’d suggest writing up an email template to use in these situations. That way you’re not writing a new email from scratch. Also, you can use Google Alerts to automatically find mentions of the product name without having to Google it manually on a periodic basis.
To show articles that mention the company on your website, I would not rely on an automated plugin. Just copy and paste a little excerpt (not too substantial, to avoid copyright concerns and stay within fair use) from the article and then link to the full version. This could be part of your main blog, or a separate post type like Press.