The first time you use a mesh for a melt, it doesn't spall until it cools. By that time, the glass has hardened enough that any black specks of metallic oxidisation just land on the top of the melt and can be brushed away.
But, once a mesh has been fired previously, it can spall and drop little bits at any time during the firing process, so some of the bits get embedded in the glass.
The only way I have found to prevent this is to sandblast the mesh between firings to remove any loose flakes of metal. This is time consuming enough that you may wish to use a new piece of mesh for each melt. The alternative is to ensure you are using stainless steel as the grid.
There are several options for grids.