Galway City Museum says it has notified the local authority of "issues" relating to the unsuitability of its environment for displaying the 19th-century Claddagh cloak.
The cloak, which had been on loan to the Claddagh-based institution, was returned to the National Museum of Ireland some weeks ago.
However, the Galway museum points out that the decision was taken on its initiative as a result of continuous environmental monitoring.
Absence of adequate ultra-violet screening on the €10 million building's windows has been identified as the main problem. "Following museum best practice, as soon as it became apparent that the particular environment was not suitable for the cloak, Galway City Museum informed the National Museum of Ireland in relation to this and returned the cloak," the city council has said.
Fine Gael councillor Pádraig Conneely has described the Galway museum as "another white elephant" and a "glorified art gallery" with very few actual artefacts.