The red mini carabiner in the picture below is from my pull up rope (the black paracord). Once the bow is up I attach the mini carabiner just outside the girth carabiner. When I get down I pull the paracord and it pulls the rope tag end back down through the carabiner. It either loosens and drops or comes thru and drops. Either way the rope is free. I used to attach it directly to the carabiner but I sometimes had trouble pulling it loose since in order to get slack you've got to pull the tag end around the tree and overcome all that friction of the girth hitch. Sometimes the loop is set to tight for that to slide around easily. This way the only friction I need to overcome is the tag end sliding through the carabiner.
You'll notice that I back up the Safegaurd with a slip knot set back into the bridge carabiner and then route it back up to mini-biner just so the tether/rappel rope hangs straight down the tree. Obviously this is all undone before rappelling.
View attachment 7131