The trick to putting it back on is to guide your fingers to the same level as the clips, and then when you put the case down move your hand from the left side of the case to the right side of the case; applying pressure when you reach the area where the clips are.
You only need to remove the tape to the edge of the flap. This is enough to be able to pry the battery connector up.
Another solution is to use a hex key. I also forgot to get needle nose pliers and found a multi-hex key to do the trick of bending the new screen’s hinges into place.