Iguanas sometimes get exotic appetites, possibly due to their captivity.
I would remove the eggs. She has absolutely no attachment to them, unlike a hen has to her eggs. She does not need some mysterious nutrition from her eggs. It's also a widespread and proven belief that green iguanas must eat nothing from the animal kingdom.
About handling, IMO it's safest for both of you if you give her space for a week or two. As long as she has fluctuating hormones, anything can happen.