The only thing that can be treated with dermal filler under the eye is when a tear trough is present. A tear trough is a deficit between the lid cheek junction, that starts from the corner of the eye. A tear trough can be caused by a natural deficit, or it can become visibly present from the ageing process.
When we age, the medial malar fat pat in the cheeks are the first to atrophy and decline down the face. The drop of this fat pad is then what causes the tear trough to become visible. In this case, the tear trough can be treated with dermal filler, and the anterior cheek, to replace volume that was lost. Therefore, correcting the tear trough.
If it is an actual “bag”, this could be caused from a number of things, that will need to be assess in person. It could be a herniated fat pad, or festoons caused from fluid. These cases would need to be referred to a plastic surgeon for assessment for potential surgery (lower blephroplasty).