Regarding the filter itself, you should be aware that those have a preferred mounting orientation. Quite often, you’ll find an arrow on the side of the filter but the meaning of the arrow depends on the manufacturer! See this post also for more details:
As a general rule, I avoid cleaning unless necessary. And if you want to clean I would start with the less mechanically invasive approaches. First, I’d suggest blowing clean air first (be wary that compressed air needs to be filtered to avoid oil particles to soil your optics). Try to blow the air in a way that the dust that comes off won’t fall back onto the optic. For example, if its a camera I would hold it with the sensor facing the floor, and gently blow air on the side, hoping the dust will then fall to the ground. Be careful with canned air also as it has solvent that can come out and also make a mess of your optics. Photography people use these “air blowers” that avoid this problem (just google that term). If air isn’t enough, I’d try to “dry” wipe gently with a lens tissue, always starting from the center of the optics and going in circles towards the edges. You want to push the debris to the side and those could scratch the surface, and it is better to scratch the edges of your lens as opposed to the very center. Lastly, if it is still not enough (and you ruled out a crack or a scratch), you could try a light solvent such as isopropyl alcohol (IPA). I like to dilute it with distilled water (70% isopropyl alcohol) so it evaporates more slowly and is less likely to leave streaks. The best is if the surface of what you are cleaning is accessible, then I would simply put a lens tissue on top of the surface, pour a few drops of IPA, and then pull on the tissue parallel to the surface slowly. The shear force will clean very nicely.
A few things to keep in mind, if the dirt is in focus on your images, then it is in a location conjugated with the image plane. Usually, filters are not placed in such a location and are not likely to be the culprit. If indeed the dirt is sharp on your image, you may want to try to rotate your camera a bit if the dirt remains in the same location of the camera, maybe it is coming from the camera then. Some time ago I wrote about this on my website:
Lastly, if you asked about cleaning the confocal disk, I don’t have any advice to give as I’ve never done it myself. But I’d be cautious about doing something like that, it could be that they turn in a protective atmosphere (but then again, I don’t know for sure), and they would have to be returned to this atmosphere after cleaning.
I hope this helps, take care,
Omni