I have to agree with Robin and get them cleaned up and dried off and they should be good. The veins aren't the stongest looking but they are there.
Another way to keep them dry until you get your order in is to just raise them mesh you have now. You really only need it to be high enough so the eggs don't get wet again. I'm sure you can find something around the house that will sit between the mesh and the substrate. Shot glasses come to mind, bury them in the medium enough to hold tight and then place the mesh over them. Just make sure the eggs are over the glasses as to not sag and get wet.
Again, you could use any number of house hold items for this. Good luck and keep us posted.
Gavin