If they are attached to glass you can razorblade them right off. If they are attached to rocks and you just want to move the shrooms
but not the rocks then cut them as close to the base as you can and they will regrow their little stump in the new tank. Conversely, the left-behind stump will grow a new shroom too.
Better yet, when you cut them off, cut them into pie shaped pieces taking care to include a piece of the center of the animal with each cut and drop them into your new tank for lots and lots of new shrooms