When getting my boat ready for the season I noticed that the ground wire between the motor and transom assy were burned on both motors, nothing else had any damage. Has anybody else ever had this problem?

How about grounds from tabs or other metal in the water ?

Hard to believe galvonic. Are you in salt ?

Maybe lightening strike in the water nearby.

Fresh water, not sure how long they have been that way. I replaced with heavey braided ones. The insulation was gone and the starboard one was separated