IF the client comes back and says "We're dissatisfied with your product" - that's one thing.
But "I showed that code we paid you for to someone else and they said it sucked" is unprofessional and pointless.
The only response I can think of was "That's interesting - could you perhaps give me some feedback as to what ways you were dissatisfied with the app?"
It's a great marketing strategy for the second-opinion consultant, though. I actually have been in this exact position. I entered into an ill-concieved "startup" project with someone who I considered a friend. It was a specialized e-commerce app that involved interfacing with some proprietary mainframe systems I had never worked with before. He thought I was taking too long so he hired some random guy from the internet to review my code. The guy said my code sucked... then turned around and said he would fix it, for about triple what I was charging. This sort of ended the business relationship (and friendship) between myself and the other founder. My old partner ended up hiring the other guy and paying the 3x rate, and the guy didn't even work on the hard part, interfacing with the mainframe! It ended poorly for me, but I learned a lot about how to market yourself as a consultant from the other guy: charge a lot, say the working code sucks and needs to be rewritten, avoid doing anything with a large technical risk, etc.
But "I showed that code we paid you for to someone else and they said it sucked" is unprofessional and pointless.
The only response I can think of was "That's interesting - could you perhaps give me some feedback as to what ways you were dissatisfied with the app?"