This is a bit complex, AM:
I know you didn't say that you were talking about yourself here, but to make it easier to reply, let's say it's you. If the "business associate" is a fellow employee of the same company as you, and the favor advantages you in that company, than the business associate is violating corporate ethics by presenting a bill. If the associate is your boss, it's technically extortion, and if you pay off, it'll never stop.

If the associate is outside your company, and the favor helped you to get the associate's business (or some other business), the demand for a payoff could be construed as "commercial bribery," which could get both of you into trouble if you paid. The exception might be if the associate posed it as a "finder's fee," and your employer pays finder's fees. But since the associate posited it as a "favor" to begin with, it's on doubtful grounds.

I'll share a broadly (but not directly) parallel experience my wife and I had recently:
Our home had been on the market for about a year but wasn't moving. We told our realtor that we were going with another realtor who had more clout in our town. She got very pissed off and cited the money she'd spent promoting our home (open houses, ads in local papers, brochures, etc.) All of those expenses are out of her (and every realtor's) pocket, and nothing in the contract that we signed required us (or any seller) to pay for them--whether or not the house was sold. She later presented a bill. It was unethical. But, despite her bad behavior, we tried to "do the right thing." We made a substantial donation in her name to a charity that she supported. I wouldn't do that in your case if the "associate" is employed by the same company as you.

As for Vito Corleone: he would have made the "associate" squirm by a subtle show of his greater power. If he weren't more powerful, he'd send Luca.