Their site is just a landing page, there’s no login option or anything like that. Their business is a smartphone application.
Edit: Gmail uses SPF, DMARC and DKIM signing so spoofing is not possible if their email services are configured properly.
For now, I do not want to announce the name of this company publicly.
If they don’t want to solve it amicably, then I will do so.
Anyway they should configure their systems to reject unsigned e-mails and providers that don’t have a proper SPF configuration. SPF (Sender Policy Framework) allows you to make sure that the message was sent by an approved server and was not forged by some hackur.