How should management go about deciding what part of its budget it should allocate to ensure good customer care/relations?

Good customer service does not directly goes trough the budget. In hospitality mainly you need to use that budget to the quality of the food you serving among that most important is that customer feel welcomed , happy and cared and that is the most important thing -service. the way you great them and treat them , even if you know you made mistake or having quality below standards you always have to show to the customer that you care about them and their satisfaction ,and they will appreciate that honesty and genuine caring no matter what mistakes you made during the service.

It should be kept to a minimum if these "care/relations" fall ouside the scope you are dealing with, I would say less than5%