The anonymous screening of application can reduce gender parity pay gap, but it can also increase it.
If for example, the employer is looking for candidates with specific skills coupled with a number of years of experience, it is possible to discriminate females, as majority may be having less years of experience due to leaves taken during maternity leave days.
For example, I know of my age mates, who have taken more than a year out of job market either due to maternal health complications or deciding to concentrate on raising their children.
Such cases, may end up being allocated a pay which is too low compared to their male’s counterparts who have been in the job market through out.