I am a huge cheekfreak, I got to see them in the spring. It was an awesome show. There’s definitely a connection between TMBG and Cheekface. (And that’s not just because of the Ana Ng cover.)
Cherkface shows a bunch of different influences. Some TMBG, some Talking Heads, some CAKE, and other things. I strongly suggest listening to basically everything they’ve released just to appreciate the lyrics. Some of the lines are weird jokes that only click after you’ve heard them a few times.