It really comes down to individual taste. Personally, I prefer them cleaner, however, there are others who like them grungy as it makes it more "antique" looking (see tks3 from my previous post about "curio lovers"). To answer your question, I can't tell from the image if there is a problem developing.
As this is probably among the top 10 most important known tsuba, doing anything to it is probably fraught with political implications. You might recall the controversy over the cleaning of the Sistene Chapel ceiling. Many objected, and much scholarship was undone as it was discovered that Michaelangelo's work was not as dark, mysterious, tortured and moody as some wanted to believe. This interpretation was entirely due to the dirt, wax, smoke and over-painting covering it up.
That said, it is possible to over clean a tsuba. It should have a sense of age and elegance. It takes practice and judgement to conserve a tsuba - I see it as being the equivalent of polishing a sword. However there is no formal apprentice system to teach people how.