I have a question related to a mole on my upper eyelid.

The mole can be removed by a cosmetic dermatologist or plastic surgeon with expertise around the eye. Best, Dr Emer.

Removing a mole near to the eye or along the edge of the eyelid requires expert care.  Seek out a board certified, fellowship trained Oculofacial Plastic Surgeon -- an expert that can work precisely and safely near the eyeball.  I have had patients travel from around the country to have me treat them for this kind of challenging removal - especially after they were turned away by dermatologists, general plastic surgeons, and family doctors.  I have removed thousands of moles from around peoples eyes throughout my career. 
You have no photos posted, but in my office eyelid moles and growths are removed under local anesthesia, and takes about 30 minutes. It is a painless procedure, and after-care would be some cool compresses for a few hours and a prescription for a special ointment that is safe for use around the eye. Full healing takes 6 months, but most of my patients with this sort of removal look great in about 3-4 weeks. Most have minimal scarring. The key is to remove these without leaving a notch or scar at the edge of the eyelid and to not damage the eyelashes.  Your mole is in a delicate, highly visible area on your face, so make sure you are comfortable that the surgeon you choose has extensive experience with these sorts of mole removals.
Best of luck in your search!
Damon B. Chandler, MD
Harvard-Penn Trained Oculofacial Plastic Surgeon

Thanks for your question.  It depends on whether or not the lesion is a little benign skin tag, or truly a mole.  If your dermatologist thinks it is a mole, you might want to have it removed and sent in for pathology (evaluation under a microscope) to make sure it is not a skin cancer.  If it is not too close to the edge of the eyelid near the eyelashes, some skin tags can be removed carefully with cautery, but I would make sure you are seeing a board certified dermatologist to have it evaluated first.
Best of luck!

I would not have any mole removed strictly by cauterizing or burning it.  A specimen needs to be sent to the lab for pathological examination.  What if the mole was cancerous?  Doubtful, but possible.