irishpapermoney.com

Very few of these notes around but here are two good images of the type of stamp I am wondering about. Any suggestions as to their purpose? Was it a duty stamp, the bank's own identifying stamp applied when the note was issued? Not seen after 1797 on any BoI note as far as I know.

There is a document in the British Museum which may answer this question. The document indicates that the ‘mark’ was introduced in 1783 with the purpose of preventing forgery.

And this, right on cue, is a close up of one on a 1797 forged guinea note! Perhaps by this point the bank had realised the idea wasn't working?

Yes, it appears that the Bank realised that their security device was no longer deterring the forgers and stopped using it in 1797. Here is a notice issued by the Bank in a contemporary newspaper which indicates that the Bank had concerns about the forgery problem.