AFAIK the bank is obliged to seek more info on transfers over a certain threshold, i think its €10k.
As a non resident you have no tax obligations but it may be advisable to contact your bank and inform them of what your situation is in case it throws any red flags up on their system when larger payments come in from overseas bank.
If you're not trying to transfer from Isle of Man, Jersey, Guernsey, Switzerland and Liechtenstein, there should be no red flags raised and you should be fine.
In 2011 Revenue obtained a High Court Order to compel Irish banks to hand over details of anyone who received a transfer of more than €5,000 going back 12 years from any of the above countries and AFAIK that's still active.