What is it called when you have eye surgery where the bag of fluid behind the eye is removed?

Not sure about a bag: Baggy lower eyelids can be corrected by plastic surgeons or ophthalmologists in a surgery called blepharoplasty. There should not be a bag of fluid behind the eyeball.

Vitrectomy: Removal of the vitreous, the material that fills the eye behind the lens and in front of the retina, is done for a number of reasons, including bleeding, infection, to treat or prevent retina detachment and rarely to remove floaters from the eye if they are severely disabling.