Eggs will always stick unless the pan is hot when they hit it (no matter what the pan is made of) so my recommendation is to heat the TM bowl until it has reached temp, and then put your egg(s) in. However...if the eggs are in with other ingredients, it should not matter.
Usually sticking occurs if there has been a recipe malfunction...you have added time to the recipe for example, or used a higher temp than recommended, or the speed was incorrect...however if you do have a catch, a non-stick scourer is fine to use as already explained in this forum.