There is a group that believes you should clean it off and some that I have seen look a whole lot better afterwards. They use various chemicals to get rid of a century of mold or algae.
Some people just use a whiting agent, like chalk or shaving cream to fill in the indentures of the letters and then photograph the stone, hoping the difference in color will make the letters visible. This is supposed to wash off and after you get the photo the stone will look like it did before.
There are others who say you shouldn't do anything to the marker, thinking the chemicals will destroy the stone. I am not sure what is correct, although I would tend to believe granite or marble can take a lot without any permanent damage.
The question is what good does a marker do that is not legible? If you can't read it, future generations will not even know who's grave it marks. Seems to me it makes more sense to do something to mark the grave, using caution, but with it being an ancestor's grave that would be something most would not argue with. I think the important thing is that we leave the graves marked out of respect for the ancestor and for the benefit of the future generation.
If you want to clean a grave marker there are a couple good web pages with guidance.