3:24 in this video
One little extra movement can take the TRX Push-Up to the next level.
When you hit the bottom of the Push-Up, all you do is extend one arm to the side, pull it back in and repeat with the other arm before pushing up back to the top.
This will force your core to really turn on and keep your body straight as well as light up one side of your chest at a time as you're forced to balance on a single arm.
While a strong upper-body is nice, it doesn't mean much for most athletes unless they also have a strong core.
A strong, stable core allows you to express that upper-body strength efficiently and explosively.