6,184 pupils have received higher marks after they were wrongly downgraded due to coding errors with the system, which Canadian contractor Polymetrika was involved in.
Education Minister Norma Foley has asked for an independent review of the calculated grades system once the process is complete.
Labour's education spokesperson, Aodhán O'Ríordáin, says there are still issues which a state inquiry could look at.
Polymetricka
He said: "Who made the decision to cancel the written Leaving Cert? Why were those decisions taken? Who decided that Polymetricka were the best group to go with?"
Mr O'Ríordáin feels these questions need to be addressed with an inquiry.
In total, 6,184 students will see their grades improved with the mistakes in the calculated grading system now rectified.
This will result in 340 students moving from a H2 to a H1 grade while 892 will go from H3 to H2.
Being moved by a single grade is the equivalent of a jump of around 10 CAO points.
Ms Foley had previously estimated that around 6,500 students had received lower grades than they should have due to the error in the calculated grades system.
The coding error could have resulted in a similar number receiving higher grades, but Ms Foley said these marks would remain the same.
New CAO offers may well come as a result of the clarification in grades. However, students have been warned that they may be forced to defer for a year in courses that are already fully subscribed.
Minister for Higher Education Simon Harris has been engaged in talks with third level institutions over funding for an additional 1,000 places in college courses.
