To clean the work, you can simply take a microfiber feather duster to it occasionally to prevent dust buildup. If dust does collect, a handheld vacuum will take care of it.
In the case that dirty hands touch the work, the rope can be carefully hand-washed with mild soap and water or with a Tide pen. For more intensive cleaning needs, the rope can be cleaned with disinfectants like bleach without fear of color loss or degradation, but avoid contact with the wood surface.
Here's more info on how to clean specific stains: https://www.sunbrella.com/how-to-clean-sunbrella-fabric