Hi Zvika,
Thank you for your patience. It turns out that I did not completely understand what the ABA is, after all. I now understand that if it is from my company's check then it will be the same for all checks paid out to vendors.
And as I understand your comment, it seems that this information is not stored anywhere in Ax database, just on the MICR printing where it cannot be separated from other text.
I will keep that in mind for future purposes.