Confusing wording in the legislation - which was intended to apply only to first-time buyers - actually exempted all owner-occupiers who bought homes last year.
It was estimated that up to 3,000 people paid the local property tax without realising that the legislative anomaly exempted them from having to do so.
In response to a parliamentary question from Fianna Fáil finance spokesman Michael McGrath, Finance Minister Michael Noonan confirmed that 1,500 people have been written to so far by Revenue over this issue.
Of those, 600 have submitted claims to be exempt from the tax. Revenue said around half the claims have resulted in refunds.
It has yet to contact the other 1,500 who may be entitled to refunds but said it will do so in the near future.
"Given that the Revenue has known about this issue since last Summer, it is a source of concern that half of the property owners who bought a home in 2013 and who may be entitled to an exemption from the Local Property Tax have still not been contacted by the Revenue," commented Deputy McGrath.
He said that people who should not have been billed for the property tax should be given a refund without any further delay.
"Anyone who bought a property in 2013 and paid the property tax should take the initiative and contact the Revenue to see if they are entitled to a refund. In addition, they may be exempt from the tax until the end of 2016," Mr McGrath added.