XADC Current Sensing Reference Design
I want to understand why, for the REF output of INA333, there is a
  pull-up of 0.05V?


The minimum voltage that the INA333 can produce when the negative power rail is attached to 0 volts is typically 50 mV so, if the REF pin were tied directly to ground, the output would not change for inputs that might otherwise have caused a 50 mV rise in the output.

By attaching REF to 50.7 mV, it means you get linearity from the "null" input condition upwards. The price you pay is that you have a 50 mV offset but, given that your circuit implies that a differential ADC is used, this is of no-consequence.