No set answer to this - depends on the team and their process:
One team I worked in the assistants would do an eligibility check, the officers would do the screening
Another team I worked in, assistants would do the pyschometric scoring filters, the officers/manager/head of would do the application screening
Another team I worked in, everyone screened because of the volume of applications (even people outside of Grad Rec, but in other areas of HR)
Another team I worked in, lawyers used to screen after someone in grad rec filtered out the clearly not good enough applicants
Another team I worked in, I literally read every application
Other firms outsource their screening to people like me or to larger RPO recruitment companies (increasingly common these days). Until about 4-5 months before started here, I was doing that for a few firms (one US, one regional, one national).