While the ANA and those content to parrot them will say that yous should NEVER clean a note, this is nonesense.
Many inexpensive notes are out there and cheap because they are in appalling condition. filthy, torn wadded up in a ball.
I have purchased many of these for a song then put some work into restoration to produce a note that, while far from UNC, is quite presentable.
The first step, almost universally, is to soak the note for a few hours in a luke warm solution of water and Dawn dish soap. I use about half or less of the amount of soap I would use to wash the dishes. I use Dawn because it is most effective at breaking down the soils typically accumulating on banknotes. Additionally, the soap will reduce the surface tension allowing the water to penetrate the fibres of the note paper.
Once the water begins to take on a dirty appearance I change it for clean water. I repeat this until the water remains clear.
Next, I place the notes between two or more sheats of blotter paper and press the sandwich under a modest weight. (My 3 volumes of SCWPM are just about right) I leave the stack over night then change the blotter paper for dry sheets. This process I repeat several times.
The result is a much cleaner if still imperfect note in a flat, presentable condition. By comparing the note after this treatment to its condition before, it's difficult to argue that the note has not been improved.
This process was gleaned from papers published by the Smithsonian and others. If you wish to review this process and others for proper conservation of banknotes and other documents I recommend the NORTHEAST DOCUMENT CONSERVATION CENTER