Update- after sending them a warning email about GDPR I got an instant response back that I've been removed from their mailing list. But it's a copy and past auto-response in my opinion because I asked them to remove my domain entirely and they haven't acknowledged that. The wording was:

"Hi

Thanks for getting in touch! We have now removed you from our system and will not email you with business opportunities again.

If you do change your mind then you can sign up any time as a Pro at Bark.com and choose exactly which types of leads you want to hear about.

Kind Regards,

Bark
The Bark Team
www.bark.com
team@bark.com"