You are dead meat. You'll pay for this. If Fluffy is missing or in kitty heaven, this is no idle threat. Homeowners can become understandably furious if something happens to their favorite pet. The legal threat, however, is minimal.
Actual damages are limited and hard to evaluate.
Do not underestimate the emotional angst. This kind of thing can terminate the relationship, even if things were perking along just fine. It is the owner's responsibility to make sure pets are secured throughout the construction period. This happened to me early in my career. Clients were either convinced that I actually owed them this, or they were miffed about something else and saw this as an opportunity to get revenge.