What should I do with the ash (cross) that the priest marked on my forehead during the Ash Wednesday? Wash it away with water, clean it with facial tissue and throw it away or leave the ash until it goes away gradually.
There is no official teaching on this. Some people clean it right away. Some leave it on for the whole day.
Some people leave it on as a sign to testify to others, reminding other Catholics to get to Church, and possibly drawing the interests of the non-Catholics to ask about it and from there to find the opportunity to evangelize them.
Some people clean it up, practising the injunction from Jesus, not to look dismal when fasting, but put on oil on the head instead. This is also commendable as it could nurture humility and inner recollection when done properly.
As I said, there is no preference…