Royal Caribbean International RCI New "mandatory" tips amounted to $71/meal in the dining room Nassau Texas

We traveled (two people and a 6mo baby) and were charged $283.50 for 6 days in gratuities.  We cannot find any agreement where we approved this.  We called Royal Caribbean, they said they have no docuement where we agreed to this, however they said this is mandatory and billed us for this after the cruise (it was NOT included or mentioned in the amount we payed up front).  We only ate in the dining room 4 times, so we effectively left at $70.88 tip per meal.  They claim they cannot provide a refund and this is mandatory.  

In addition to my frustration about this bait and switch on pricing, the math doesn't seem to add up.  If waiters are getting $70+ per table in tips then they'd be making half a million USD per year if they work just 20 tables a day!  Royal Caribbean must be doing something under the table here.