If it is inconvenient to lap under runing water, at least thoroughly clean the plate (a bristle brush helps) after use, and place the hone on top of the plate while lapping - any small bits then get a chance to fall into the troughs, hopefully.

As long as the marks are below the level of the surface (which they will be) and light, then its probably nothing to worry about - I see them on mine, too. Finishing lapping with long up/down strokes rather than figure of eights or circles reduces the impact of the lines even further.

If you really want them to be spotless, rub the hones together as a final measure, but make sure you really clean the surfaces down.

Regards,
Neil