Much wisdom here, and no need to repeat it.
My only suggestion is to choose words carefully- in particular, the word "abuse" can carry an accusatory tone and imply that the person caused the damage with knowledge or intention, and now expects you to fix it. While that might be the case, it is just as likely (or more so) that it was more a situation of neglect or lack of knowledge or even possibly a situation that the customer couldn't control.
In the interest of avoiding hurt feelings and bad press, I think just explaining what the warranty does cover (workmanship, material flaws) and that this damage was clearly caused by the conditions the mandolin experienced (too much humidity over time, string tension after the problem was noted, etc.), might be a way to keep things clear while avoiding accusing the customer of abuse, neglect or stupidity.
Otter OM #1
Brian Dean OM #32
Old Wave Mandola #372
Phoenix Neoclassical #256
If you're gonna walk on thin ice, you might as well dance!