My sisters dog bit me, so I shot it, how do I make her shut up?

My sister asked me to feed her dog while she was on vacation and I agreed to do it. The very first time that I was there it bit me so I dragged it outside with my brother in laws shotgun and put it down. My sister won't stop telling everyone that I murdered her dog, which is stupid because at the very least it was self defense. How do I make her shut up? I have offered to get her some sort of rodent or fish but she doesn't want that, she just starts yelling again. How do I get her to stop slandering my good name?