I have dealt with both grease splatter and mold (ugh) on bags and I think it looks more like grease. The spots are pretty round and uniform which makes me think grease. I haven't had much luck with grease stains, but I am sure someone has. I have also tried cornstarch and spot applying dawn dish soap without success.I think they could be grease. Some people have been successful in removing grease spots. I think someone bought a product specifically for that. I've tried cornstarch but it didn't work for me.
If you think it's mold, there is a product called concrobium mold control that comes in a spray bottle (you can get it in hardware stores) that is excellent for killing mold. I have sprayed the inside suede side of bags with it and have also done vinegar rinses. Both work.