You're supposed to use electrical tape under tension to end the wrap; then you use those finishing strips on top of the electrical tape to create a cleaner finish to the wrap job. Since you don't put as much tension on the finishing strips as you do the underlying electrical tape, you don't run into the peel-back issue that you get with tensioned electrical tape.

If you don't want the Bontrager logo plastered on your bike, you probably shouldn't have gone with Bontrager bar tape since their logo is embossed into the entirety of the bar tape.