How to Remove Mysterious Dent in Thigh?

Based on your description you may have a dermatofibroma which can have a firm periphery with a dimpled center.  If so, this will not respond to fat grafting.

This question is a bit tricky to answer without knowing a little more information about the "dent."  A picture may help some, but my guess is you need to meet with a plastic surgeon so he or she can examine you and feel the dent his or herself.  If this depression is an area of little or no subcutaneous fat, fat grafting might be an option.  Generally, the likelihood of transferred fat surviving is better if there is already some fat in the area.  If the dent is more extensive and involves more structures than just fat, fat transfer may not be the answer.  It may be possible to excise the entire area, but this will leave a scar.

From your description, it sounds like you have an area of depression where the skin is close to the underlying muscle with no fat in between.  Fat graft survival (called take) is best when there is some fat already.  If the surrounding tissue (bed) is all fibrous such as scar tissue with no fat around, fat graft take is poor.  I suspect if your dent is treated fat graft, the result would be less than satisfactory.

If the dent area is small and you don't mind a scar, the area could be removed completely and the edges with normal fat thickness brought together.   This would eliminate the dent for sure and result in a smoother contour but at the expense of a scar.  Otherwise, I would leave it alone.

Fat injection grafting would be the only treatment approach. Your description of 'lack of fat' underneath the skin defines the problem and how it needs to be treated. Why it is there will never be known. It is an isolated area of subcutaneous fat atrophy or lack of development.