I suspect the debt is that at some point the Hunter owes the Prince of Gold a service and the degree of how open-ended that service is something we can figure out? I think Anaphiel would have allowed the Hunter to put some caveats on what he'll do, but not so many that the service would be useless.

(I think he admires the Hunter's brash courage and that's why he's letting him place those caveats. He's generous to those he likes.)