I had another bought Recaptcha module and that was working just fine with the same keys on this domain. However the TB module throws an error: Uncaught Error: Missing required parameters: sitekey
But the keys are 100% correct, I triple checked and when I reinstall the other recaptcha module, all works well. The site runs in a subfolder and on https - maybe that causes some issues.
UPDATE: the problem is in fact caused by another module (Form Builder) that also uses the recaptcha library, when I switch it off the TB recaptcha module works as expected.
Now I am wondering if it is possible to use both modules....