I have a shapefile in ITM and I brought it into ARCGIS. In ARCGIS Pro some of the layers are in ITM and ome are Irish Grid. I ahve changed the basemap to ITM. I thought the shapefile was slightly off as one of the points were within a buffer when I knew it shouldn't be (purple icon). As the shapefile only had four points. I created an excel sheet with the four points and added them to the map (Blue icon). These locations have mapped correctly.