Markers work well when you need to write or draw a bold, clean mark, but often the marker can be difficult to remove it if gets placed on the wrong surface. Plexiglass is nonporous and fairly easy to clean and care for, but markers leave behind a strong residue that is nearly impossible to remove with most household cleaning products. Instead, use items that directly attack the marker residue without damaging the Plexiglass surface.
Rinse a cleaning eraser under water and scrub over the Plexiglass surface. The eraser is a sponge-like cleaning tool that scrubs off light buildup without harming or damaging the Plexiglass.
Mist hairspray or drizzle rubbing alcohol over the Plexiglass, and scrub gently with a cleaning rag. Continue, adding hairspray or alcohol as needed until all residue is removed. Use whichever you have on hand, but keep in mind the hairspray has a lower alcohol content so it may take a bit more time to remove the marker residue.
Wipe the area with a damp rag and dry the Plexiglass when all marker is removed.