He paid them for it, and they let him because of it. They found him sus because they did stuff to their head and didn't understand the significance.
I can feel sympathetic for Novak. I can compartmentalize that he's killed a bunch of people as part of his job, and he's also had his daughter killed. I hope the blonde young inquisitor tells him the truth soon so he can start progress the story again.
I'm impressed with Bardeni's plan. That said, healthcare was shit back then so I'm not sure how long he'd expect the beggars to be alive for, and I imagine tattoos would also be a bigger infection risk back then compared to today and that doesn't help.