Is there a better way to remove fatty tissue from back of neck without surgery or leaving an ugly scar?

Thank you for sharing your question.  The first consideration is in diagnosing the cause of the fatty tissue.  If it is due to a solitary mass (lipoma) the best treatment is surgical excision which requires a small incision.  If the fat is diffuse, liposuction can be performed to reduce the amount of fat present.  One other option, thought it would be considered off-label, would be to use Kybella injections to "melt" the fat away resulting in minimal or no scars.  Be sure to see an ASPS board certified plastic surgeon in consultation. 

The treatment for a fatty deposit on the back of the neck would depend on what is causing the mass.  Sometimes, a lipoma can develop in the area.  In other instances, there may be diffuse increase in fat in the area, also called a buffalo hump.  The usual method to remove a lipoma would be with surgery to excise it.  If there is a buffalo hump, this can be removed with liposuction using a very small incision.  In either case, the scar can be minimized so that it is not unsightly.  

Liposuction is probably the most reliable way of removing excess fat with minimal scars. The scars from liposuction are usually small.  Does however require surgery.
No surgical approaches like Coolsculpting (cryolipolyisis) would be difficult / impossible on the back of the neck.
Kybella is not something I have used and it is not currently licensed for this application.