Wheel Bearing replaced - ABS AVC light now on

Yes this the metal dust shield with hole that needs to be aligned with the sensor. It can be removed if you take the axle off again.

The abs sensor is selling used on eBay for just $30. I would still change that first without paying anything more for troubleshooting. Very easy to change

 

I would definitely get the axle nut torqued to the proper torque and make sure it is properly punched to lock it. That is not a nut you want to ever come loose on its own. I would also make sure the mechanic replaced that axle nut, because it is not recommended that you reuse it. They are also pretty cheap so there is no reason to.
If you don't want to fix it yourself I would look for another mechanic. I would not take the metal cup off the wheel hub that protects the sensor. I should not be causing a problem if the job was done properly. It keeps crud out of the sensor and the tone ring on the axle. I would say either the sensor in not installed correctly or he has damaged your sensor. I hope he has not damaged your sensor because it is an expensive part, but easy to replace as long as the bolt that holds it in place is not seized.