To answer your question, "should I make up a reason?" No, that is fraud. Why on earth, having created a paper trail with TK that the damage was caused by an air carrier, would you then make a contrary statement to another merchant.

I don't think that the Montreal Convention yields much here. The question is whether TK is responsible for the damage and it is not an unreasonable delineator to maintain that damage to the exterior of a suitcase can reasonably be noticed prior to departing the airport.

What is the repair estimate here? Are you arguing about $30 or $300?