As someone who has to approve expenses and educate the staff about what is and is not appropriate at my own place of work...
I would tell folks to expense the $100. The $20 is their benefit, similar to frequent flyer miles or some other kickback from a supplier.
I would tell them that I expect them to disclose the benefits that they are receiving to their supervisor. Why? Because while disclosure isn't a cure-all, having incentives and the like out in the open is helpful to make sure that business decisions are made in the best interest of the company and not the private individual. In other words, don't steer meetings to an iDine (or similar) restaurant. If that's the right place for a meeting, great -- but be careful not to make the decision for personal gain at the expense of the company.
(I know this is a small dollar amount involved, and my usual schpiel refers to much larger things. I have a supplier who regularly hands out pre-paid dinners for 2 at the nicest restaurants in town -- I know this supplier is spending thousands of dollars wooing a handful of employees. But the principal is the same and these things can add up.)
At the same time as the individual can earn this benefit and keep it, I'd expect them not to nickel and dime the company either, or overspend while traveling just because they can. It's a mutual respect thing.
Oh, and our employees can keep their Discover card cashback, too...