That sure is interesting! Brings me back some old sweet memories.
1) Petra as a puppy, growling at me the first time when given a bone. Worked on instilling trust with lots of drop its using valuable treats, starting with low value things then building up to things she would find on the ground outdoors and indoors. One day, I dropped a pen and didn't notice. Normally she would snatch it and go lie down to chew on it, and that one day instead she grabbed it, brought it to me and dropped it on my lap looking at me with anticipation for a treat. Priceless!
2) I moved to this rental home where the previous tenant was a smoker. Lots of cigarette butts in the yard which can be toxic eaten by dogs in certain amounts. So I am out in the yard with Einstein picking them up. Einstein watches me and then starts picking up cigarette butts and I tell him to drop it in fear he'll eat them. At some point, I am taking a break, sitting with the trash bag open and Einstein approaches and stands in front of the bag and drops a cigarette butt in the bag! Priceless!
Take Gertie's action as a sign of deep trust towards you! Not all dogs would voluntarily relinquish something new found on the ground that is interesting.
I am not sure if dogs can think along the lines of "I will take this away from Esther because it's "bad" for her", (yet who can prove that until the day dogs can talk!) but maybe I can see it happen more along the lines of " I will bring this to my owner who is happy when I drop stuff we find".