I want to know this as well. I only embed my own tweets on my own website, I don’t need my avatar repeated time and again next to every single tweet taking up valuable space. It’s utterly redundant! It’s not like they let us even adjust the size of it.
The fact is, I’m not embedding my tweets to advertise Twitter, so I couldn’t give a monkey’s about THEIR branding. They may own Twitter, but I own my words, and that’s all I want on my website … a way to redistribute MY OWN words, and make them fit MY branding!