The Sinn Fein leader says the number of passengers being followed up at Dublin Airport is not good enough.
Just over 4,100 calls were made to check up on 61,844 passengers during the first half of July.
It follows a parliamentary question from Social Democrats co-leader Róisín Shortall on passenger locator forms, which shows just 52 per cent of calls were answered.
A sample of 6,195 passengers was taken, with 1,974 exempt from follow-up as they were transiting to Northern Ireland, or in the State for less than two days.
The calls are made to make sure people arriving into Ireland are self-isolating for two weeks.
Mary Lou McDonald says it has to be monitored better;
"Some form of effective monitoring, effective checks and balances and effective quarantine. Currently people land, they fill a form, they may or may not get a telephone call. Lots of people as you know are reporting they get no contact whatsoever."
