The HSE has said that a "catch-up programme" is now under way after thousands of children missed out on hearing and eyesight tests due to disruption caused by the pandemic.
These tests are usually carried out in Junior Infants as part of the School Screening Programme, but public health nurses were redeployed to "support Covid-19 related clinical activities".
The HSE has said that the number of staff assigned to the school screening programme is not back to pre-pandemic levels, because a "small number" of public health nurses are "still required as part of the pandemic response, which is on-going".
It could not say how many children missed out on hearing and eyesight tests, because the figures for the school screening programme are not recorded at a national level.
In a statement, the HSE said: "There is currently a catch-up programme in operation for children who missed out on the school screening programme.
"The HSE works in conjunction with the school principal, to ensure that each child is offered screening as soon as possible.
"The school screening programme is not part of the National KPI (Key Performance Indicators) reporting data set, but rather is reported at a local Community Healthcare Organisation level."
The HSE also said that if an individual teacher has a concern regarding a child's vision or hearing they can "contact the school public health nurse at any time and with parents’ consent the child will be offered a screening".
But the Irish National Teachers' Organisation has said that teachers are not mandated to make referrals to public health teams.
A spokesperson for the INTO said: "Teachers would routinely flag any noticeable areas of concern with parents, where they present in a classroom setting and regularly interfere with a pupil's ability to engage in the class.
"Teachers are not qualified to diagnose underlying conditions requiring additional support, nor are they mandated to make referrals to public health teams.
"All health screening carried out in primary schools is done with parental consent.
"Anecdotally, we understand that backlogs have increased following the pandemic, with waiting lists growing for these essential public health services.
"We continue to call for public health teams to provide more on-site support to pupils in schools."
It is the policy of the HSE to provide a national school vision screening programme to detect amblyopia, also known as 'lazy eye', and to refer a child for further treatment if required.
It also provides a national hearing screening to "assist in the identification of undetected hearing problems" that require further assessment and/or treatment.
The INTO has called for investment in "essential wraparound services for schools," which it says have deteriorated in the last number of years.
The union recently led a national campaign to secure additional investment in school-based mental health support for pupils, with a commitment from the Government to deliver a pilot scheme.