Let's say you paid for a friend's bus ride, and he insists on paying you back rather than just let it be and stop worrying about it. You even find it rude on his part that he won't just forget about it. Is there an adjective or a phrase for such kind or a person, or for such kind of a behavior?
Fastidious can have the sort of connotation I think you're looking for.
Possessing or displaying careful, meticulous attention to detail.
Difficult to please; exacting.
Excessively scrupulous or sensitive, especially in matters of taste or propriety.
"He was the sort of guy who might ring you at 4 in the morning to repay sixpence; the chap was fastidious about his debts."
I think the word stickler fits very well here, in the sense of a person who's obsessive about making sure customs and rules are followed to the letter. If I were to use it in a sentence, it would go something like this:
He was a stickler for making sure that even the smallest and most insignificant debt was repaid in full.
It carries a connotation of following a rule to the point of being slightly annoying about it.
I would say this person suffers from an aversion to generosity.
That's not an adjective, but I think the phenomenon may be too complex to boil down to a single word (cultural factors? fear of indebtedness? fear of not being able to return a kindness? feelings of inferiority? etc).
Maybe generosity averse? :)
I would call him a nitpicker, after revieing this I'm not sure whether it would be approriate: nitpicking
Someone who is "anal retentive" is a good fit and conveys the speaker's annoyance quite effectively.
Wikipedia describes it thus:
The term anal retentive (also anally retentive), commonly abbreviated to anal, is used to describe a person who pays such attention to detail that the obsession becomes an annoyance to others, potentially to the detriment of the anal-retentive person. .
Many Danes are familiar with a concept that also seems to be in play in the case of the OP's obsessive debt-repayer. They call it millimeterdemokrati ("millimetre democracy").
It is typified by phenomena such as the scrupulous analysis of a restaurant bill to calculate who owes how much, the maintaining of a log in order to track whose turn it is to wipe down the fridge door or rinse the tea cups, and the cutting of a cake into slices of precisely equal size (with the help of kitchen scales, in the worst case). You could say that individuals afflicted with this impulse are applying an ethos of egalitarian reciprocity/responsibility taken to an extreme degree.
(I hasten to add that most Danes are not quite this silly.)
Looking over the other suggested names for this attitude, I don't think any of them quite capture the nitpicking quality of millimetre democracy at its finest.