Hi ! Okay, first off, I wouldn't worry about eggs yet, you might, might see them when she is 12-18 months or more.
Second, let her have her floor time separate from Gizmo. This way there will NEVER be the chance of fertilization, nor aggressions. Just keep both out of each others' sight, and things should all be good.
Lay box:
Rubbermaid container 18 qts or larger. 2 lbs of playsand, 2 lbs of baked potting soil, dampen them together until you can get a drop of water when squeezed between your fingers.
Clamp on shop lamp with flood light, opposite side soil/sand mixture is on.
Lid with open cut for light to flood onto the mixture.
Patience.
If and when she starts, you will notice a lot of scratching and digging going on in her viv. At that time, just place her into the lay box, don't worry about feeding or watering her, as she won't take either. Once done, give her a lovely soak, and return her to her viv.
Remove unfertilized eggs, freeze and toss.
There you are. I hope this answered your questions !
Janie.