Glory,
Try what Rushton said ^^^ Stick the ME sliver on a toothpick for a handle, and hold that between thumb and one finger only, delicately.
If the stylus still doesn't look crystal clear under magnification, step up to the super-fine sandpaper technique Stringreen and I discussed just above. That and a brush will clean anything I've ever seen on a stylus.
With either tool, be slow, gentle, patient, undistracted and chemically un-altered. No caffeine or other fun juice. It's also a big help to have something sturdy as a wrist rest while you clean.
If a stylus is gunked up and you make it notably cleaner, the improvement will be instantly audible.