This depends on the kind of underwater pen and paper. The majority of dive slates can be cleaned with rubbing the plastic, either with your hand or sand.
However most of the time this method does not produce the optimal result. Many divers confess that typical plastic dive slates are difficult to clear whilst underwater.
When returning the surface, you can use rubbing alcohol, magic erasers as well as everyday erasers. It is worth taking the time to properly clean your dive slate when on dry land so that your underwater messages show up clearly.
A magnetic scuba notebook, on the other hand, is the easiest to clean with the press of a button.