you could say it in a number of ways, like to "owe a debt of gratitude" or to "owe someone a favor." A common phrase is to say "I owe you one," when someone does you a favor. It can be translated as obligation, but that's a stiff way to say it, and infers it's a kind of duty.
I can't think of any phrase like 恩知らず, just to say they don't pay back their debts