All ceramic sharpeners tend to fall part way between a conditioning and honing/ abrasive function - it's what makes them so useful. In that process, minute particles of metal will start to show as grey streaks on the rod surface. As they build up they reduce blade contact with the ceramic surface and periodic cleaning is a good idea.
Lansky Eraser Block for cleaning ceramic rod type sharpeners
We sold a large number of these sharpeners and our standard advice is to use a little scouring type cream to remove the metal particles - and to be honest that remains the advice.
However, a few people have been in touch seeking something they can readily carry with them in the field or when away from home. Several others - that shall remain nameless - have indicated that years of careful planning could be wrecked if they are discovered with 2 metres of the kitchen sink and actively looking for a cleaning product.
So for the sake of domestic content & harmony - here's an answer. Not essential, but here if you want it.
Use just like an eraser to lift off the grey streaks from the rods. Can also be used to remove tarnish/ staining from various metal finishes - eg on carbon steel blades.
£6.20 via the Forest & Hill website posted first class.