Rather than running your fingernail down the sides to free up the retaining clips, I found that using an old credit card, inserted about 1/4”, to run along the left and right side popped those end retaining clips right off with no problem. You may need to twist the card slightly when in the middle area to help pop those off.
I have replaced about 6 batteries in iPhone 5S and 6. I cut and only use about 1.5 inches of the new strip, centered in the middle (horizontally) of the battery with the end tab wrapped over the battery bottom for future grasping / removal. Those strips are very secure and don’t see the point of two 3.5 inch strips to hold it in place. I thought that they possibly served a dual purpose of securing the phone and as a thermal transfer medium to move heat from the battery to the case back. I have yet to see anyone post that there is a need for heat transfer from the strips, so to me, use the smallest length possible to secure the phone and make it an easy job for the next removal !!