"it was no business for me" what does it mean ?

Question

Memento film script

Answer 1

In English if something is not one's business that means that it is not information that the person is entitled to know or be involved with.

If I were to say that it's none of your business what I am saying to my friend that means that I don't want you to be involved in the conversation because it is not your right to be involved.

Example---

Teacher: What is it Jimmy?

Jimmy:    What grade did Sally get on her test?

Teacher: That is none of your business.

Another phrase that evolved from slang of "it is none of your business" is "it is none of your beeswax". They both mean exactly the same thing.

Answer 2

As one of the characters of the movie is a fraud investigator, it could mean literally 'nothing to do with my line of work'.

But it could also mean metaphorically "no personal concern of mine", "I couldn't care less".

Or maybe, also metaphorically, "I had no right (to do or say this)".

You'll have to figure it out from the context.