Should I tell my neighbors (an older couple in their 60's) my dog killed their cat?

It happened when they were out on errands. I thought she was well behaved with animals and didn't put her under a leash for several minutes. We passed by their yard (usual routine before doing exercises), she saw the cat and killed it.

My dog is a mix between a bull terrier and German Shepherd. That's the first time she ever killed a cat, that I know of. I've taken care of the mess but they don't know it. Should I tell them what happened?

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Or should I just let this slide? I'm going to take care of the issue and take her to training. I just don't want this to cause a huge commotion.
Should I tell my neighbors (an older couple in their 60's) my dog killed their cat?
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