I used nothing but Kodak Lens Cleaning Paper (aka lens tissue) for the first 15 years; then, I switched to Hanes 100% cotton T-shirts for about 15 years; the last eight or nine years I have started using microfiber cloths. And ya' know what??? ALL THREE seem to clean simple water and simple fingerprints pretty well. I don't think the water will have ruined the ND filter.
At times, it's necessary to use some kind of a CAMERA lens cleaning fluid, which is always applied to the cleaning tissue, and not just sprayed or dropped onto the filter or lens...you do NOT want lens cleaning fluid running down into the mount, or into the lens. Heavy emphasis on CAMERA lens cleaning fluid and NOT "eyeglass" cleaning fluid.