Prolonged bruising left me with brownish color under the eyes. Is this hemosiderin staining? (Photo)

This could be hemosiderin staining. However, seeing more of your face would be helpful. I'm not sure that any irregularity from fat grafting can be determined based on this photo, especially since we don't have any preoperative photos to which to compare. Seven weeks is relatively early after fat transfer. I would not consider laser this early after the surgery. I would wait about 6 months before considering any other treatment. Close f/u with your surgeon is recommended for

You actually look a bit lumpy, bumpy from your fat grafting but to be honest, you are showing us so little of your lower eyelids that it is impossible to know for sure.  The difficulty with lower eyelids that they are extremely sensitive to the optic of how light interacts.  It is possible for an eyelid to hemosiderin stain.  However, I am not sure that is what is going on here.  It looks like this is related to the irregularity created by the fat graft.  IPL and other systems have the potential to improve hemosiderin staining in the eyelid but that may not help you situation.  I would see how things heal long term before rushing into additional treatments.

Hard to tell if this is skin discoloration or shadowing from the residual swelling in the fat.  If you had significant bruising it can take quite a while to clear.  Sometimes some intense pulsed light treatments can help to lighten the skin.