Why is it so salty?
It shouldn't be. It may be that whatever butcher is kashering these for you is using too much salt (e.g. the same amount used on thick cuts of meat that don't have all the ridges for the salt to permeate).
So, try a second soak to get rid of the salt.
Try tenderizing with an aluminum meat mallet instead of a sodiumladen marinade and then marinate with a no-salt bottled Italian dressing.
Since the meat will continue to cook while holding on the blech (this is a thin piece of meat) DON'T grill to medium Rare, just grill on a very hot grill till 'Black and Blue' nice char/grill marks and almost raw inside. Let it finish cooking on the blech, but make sure not to seal the foil or ot will steam and lose the grilled properties you desire.
In general, grilled items don't hold up well on the Blech.
When kasherng meat, one must first soak it in cold water and then salt it on all sides for 1 hour. The salt is then washed off but since the skirt steaks are so thin, the salt penetrates into the meat, leaving you with very salty skirt steaks.
The best way to reduce the saltiness is to soak them in cold water for a short while, then rinse them off and repeat the soaking process for one or two more times in fresh cold water. T his should help somewhat, but it will still be salty so don't add any more salt when you are preparing it.
re: chicago maven
agreed...I always soak before I cook it (also hanger steak if you've ever had the opportunity, it's great)...i didn't realize it's due to the meat being so thin, I thought it was because of the corrugated texture (ie - more surface area) which is the same with the hanger...but it doesn't matter why it's salty, a soak really does wonders, even if it's for 15-20 minutes
but don't forget to dry it thoroughly before grilling it,
and one thing that bugs me like crazy, is cutting it incorrectly, it makes worlds of a difference, seriously...most of the time to cut against the grain, you have to cut the skirt steak into like three or four strips, and then rotate that, and cut that into manageable pieces agains the grain (and on the bias)