The first time I was hired to re-design a company website I thought I knew it all. With a confidence of an Olympian, I barged into the meeting room and went one by one through what I thought was wrong with their previous design. The only person who acknowledged my notes was the CEO. But the product team felt hurt, because they've been working on this for so long and now they (together with me) were supposed to start all over again.
It didn't take me long to realize this is not the way to deal with customers. Just because the rest of the team isn't paying my bills, doesn't mean that I shouldn't include them in conversations related to their previous work. The minute I showed interest, the team members noticed it and started to be willing to adjust, tweak, and acquire new ideas.
Always avoid talking bad about the work of others. They have been working on the product for a much longer time than you ever will. It's their baby, show some respect. The reason you got your foot in the door is that the client already knows that something needs improvement – that's why you're there.
Let the company send you all of their previous designs and related materials. Spend a weekend on it – do you homework and come back on Monday with precise questions. Questions like:
When it's your turn to talk improvements, discuss things you found in their materials and how you would move from there. And when you're asked for feedback, at least give them the sandwich or something.
From the moment you know all stakeholders of your project, do your best to get to know them well. You don't have to befriend everyone, but realize that in each company you work for you're building a network of professionals.
Even when working temporarily with people, you have an opportunity to connect with them more deeply. Talk to them, ask them for help. Always stay humble to their work. You never know when your paths cross again; heck, you might be colleagues one day.
Sure, this general rule saved me a couple of times. Though it forces you to learn and deliver things that you promised, it's a double-edged sword. But when the stakes are high, it's better to just come out with the truth than risking failure. Be honest and your client will appreciate it.