I'd use a razor blade to remove them. Tough or not, you do want to avoid applying pressure to the eggs directly if you can avoid it. Scraping off the jelly mass shouldn't hurt them though.
I doubt it matters if they attach to anything in the new tank, as long as there isn't anything dangerous for them to float into.
I've also had a little success placing a protective barrier around eggs where they are. Hardware stores carry a special washer for filtering wash machine water that consists of a rubber ring with a dome of fine wire mesh that allows gas exchange but keeps fish out. You just have to find a way to stick it to the glass over the egg mass. Unfortunately newly hatched snails seem to be just as tasty as eggs, and my survival rate once they leave the enclosure is... negligible. I'd be surprised if the snails would eat them once they hatch, though, if the fish weren't interested.