Flat mole on neck: Will removing it leave a scar?

Yes, you could have a minor procedure done to help the tissue on that side. You could also have filler done, by an experienced injector, who could make the asymmetry better, but you'd have to repeat this again and again. However, I really had to study your photo to see how much of a difference...

The fleshy lump is a combination of swelling and a tiny bunching of the skin called a "dog ear".  Scar massage and time should allow it to flatten nicely.  The alternative would be to extend the scar, which would not be desirable.  Best of luck.  

It is very difficult to tell from your photo what exactly is going on with your mole. To be safe, you should be carefully evaluated by a board certified dermatologist. Please use the ABCDE's as your guide for when to be concerned about moles: A for Asymmetry; B...