Although to many advanced users it may seem obvious, new laser machine owners find it difficult to remove the burn marks around cuts and engravings. 

When we started using our current laser cutter a few years back, our main cleaning method was through sanding. After that, I've read somewhere that vinegar is efficient for removing those burn marks, so we used that. The result was pretty good, but the smell less so. 

One day we thought of using plain water instead of vinegar and it worked perfectly. We are using water to clean everything ever since.

It works really nice on both plywood and MDF. 

We also loved to use it for painted MDF panels like the one in the image below. For these, I actually let the water flow over the panel and gently rubbed it with a sponge. Nice and clear!

So yes, from our experience, the best way to clean the burn marks from cuts and engravings is by wiping them with a wet cloth.