When might you expect a manager to offer a gentle reminder about hand washing?

The answer to the question really depends on the nature of the business or the company.

Let us take for example, a food chain. The crews in this business are always reminded of the importance of washing of hand in order to avoid the occurrence of an event wherein the food being served to the customer might get contaminated.

On the other hand, if the business and the position of the subject matter does not involved handling food or other materials then, it may be acceptable for them and the manager need not remind the employees anymore.