I remove the outside mesh upon transplanting, as well. There are two types of mesh they use, one is more of a fabric and the other is some sort of woven plastic. The fabric version is a PITA, are not very good for the roots, and are hard to remove. The woven plastic ones are no problem and are more forgiving on the roots.
Of course, there is no indication on the box on which ones you might have and you kinda have to know before hand. The fabric type is difficult to cut with scissors.
Have yet to have an issue with too much moisture for germ/establishment. You really only soak them on the initial expansion. Warm, plain tap water. From then on, small amounts of water when they look like they (the pellet) needs it while adjusting the cover to allow increased circulation/lower humidity as they become established.