Rather than urge guests to leave bigger tips and thank you notes, Marriott should pay its housekeepers a living wage.

As an old popular song asks: What do you get if you “work your fingers right down to the bone?” Boney fingers.

As housekeepers in the sprawling Marriott hotel chains know, that’s more than a cute lyric. It’s the truth.

These “room attendants,” as they’re called, are paid barely $8 an hour to perform a very hard, physical job, suffering the highest injury rate among hotel workers. Some two-thirds of them take pain medication just to get through their day of heaving 100-pound mattresses, stooping to clean floors, and twisting to readjust furniture in 15 to 20 rooms per shift.

Yet Marriott President and CEO Arne Sorenson publicly hails the very women he exploits as “the heart of the house,” saying his chain likes to express its appreciation to them with “special recognition events” during International Housekeepers Week.

Yes, exploited room attendants are not rewarded with a living wage, but with a congratulatory week — how great is that?

This year, housekeeper week came with “a new tipping initiative” — a scheme created by multimillionaire Maria Shriver — urging Marriott’s customers “to express their gratitude by leaving tips and notes of thanks for hotel room attendants.” Shriver says she hopes the voluntary tips “will make these women feel seen and validated.” Is that sweet or what?

Does she at least urge that this tip be the standard 15-20 percent we give at restaurants? No. Tipping between one and five bucks per night’s stay is recommended. Let’s see: At about $250 a day for a Marriott room, even $5 is a sad 2 percent expression of “gratitude.”

As for customers leaving a little thank-you note, imagine trying to buy a baloney sandwich with that.

How about this: Instead of paying Sorenson $9 million a year, make the Marriott CEO rely on customer tips — and see how validated he feels.