Where an individual’s income qualifies for the remittance basis
of assessment
This manual relates to individuals that are tax resident in Ireland but not domiciled* in the State for tax. The thread title mentions "returning to Ireland". Can you give some more details on this? Were you born in Ireland and went to the US for work for awhile? How long were you away? If you could give indicative dates for the above events (date of sale, date of return to Ireland) it would be helpful.
First things first - if you sell the US property before becoming tax resident (i.e. in a year before the year you become tax resident), then any gain on the property is outside the scope of Irish tax. Any subsequent transfer(s) of the proceeds to Ireland would be considered capital accumulated whilst abroad.
If we operate on the understanding that you will be Irish tax resident but not domiciled in Ireland when you transfer funds to Ireland from the sale proceeds, if you are remitting the funds from an account that only contains the sale proceeds, then all you are doing is remitting capital to Ireland and there should be no tax consequences (see edit note below). If the account the transfer is made from contains gains realised since 1 Jan of the year you became tax resident or income earned since 1 Jan of the year you became tax resident, then there could be tax consequences in Ireland, but relief may be available under the Double Tax Treaty.
If the sale of the property is delayed and you are tax resident in Ireland at the time of the sale, if the property was your principal private residence, then Principal Private Residence Relief for CGT comes in to play.
If you are Irish tax resident, domiciled in Ireland for tax, and assuming the sale took place before becoming tax resident in Ireland, all you are doing is repatriating capital accumulated whilst abroad and there should be no tax consequences (see edit note below).
*Domicile is a concept of general law, not tax law. It broadly means living in a country with the intention of living there permanently. Domicile is a much more permanent concept than residence.
EDIT: If you leave the sale proceeds in USD, movements in EURUSD will give rise to tax consequences.