My guess is that the company that contacted you is using one of these (Stripe requires your public key in the head of your site and linking to their JS). BuiltWith is one such service: http://builtwith.com ... NerdyData & Datanyze also: http://nerdydata.com, http://www.datanyze.com
Subscribers use these tools to find people who are trying out competing services (they are not cheap, BTW). Often, if a site only recently added JS code–for example, say, KissMetrics–you can assume they are still in the trial period. That gives you a window of time to try and sell them on your competing product. Or, if you sell a special WordPress plugin, you can use these services to find WordPress sites.
Stripe doesn't have a trial period per se, but its pretty easy to switch between the modern payment providers and if it was only recently installed, its safe to assume you don't have a lot of customers yet.